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In abstract algebra, the weak dimension of a nonzero right module M over a ring R is the largest number n such that the Tor group Tor n R ( M , N ) {\displaystyle
Weak_dimension
Index of articles associated with the same name
Projective dimension of a module, based on projective resolutions Injective dimension of a module, based on injective resolutions Weak dimension of a module
Homological_dimension
Property of a mathematical space
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify
Dimension
Concept in ring theory and homological algebra
Noetherian ring, both of these dimensions turn out to be equal to weak global dimension, whose definition is left-right symmetric. Therefore, for noncommutative
Global_dimension
Mathematical concept
space, then H endowed with the weak* (subspace) topology is a metrizable topological space. However, for infinite-dimensional spaces, the metric cannot be
Weak_topology
Natural stone that has been finished to specific sizes and shapes
detonating cord, a weak explosive. A variety of igneous, metamorphic, and sedimentary rocks are used as structural and decorative dimension stone. These rock
Dimension_stone
problem is weakly NP-complete (or weakly NP-hard) if there is an algorithm for the problem whose running time is polynomial in the dimension of the problem
Weak_NP-completeness
Hypothesis about sapient life and the universe
Bostrom counts thirty, but the underlying principles can be divided into "weak" and "strong" forms, depending on the types of cosmological claims they entail
Anthropic_principle
Polish-American mathematician (1913–1998)
University of Warsaw Known for Acyclic model Category theory X-machine Weak dimension Projective module Shuffle algebra Simplicial set Standard complex Eilenberg's
Samuel_Eilenberg
domestic labor. al-Amshati described "Abyssinians" (Africans) as physically weak slaves who often fall ill; however, they had a long number of traits suitable
Slavery in the Mamluk Sultanate
Slavery_in_the_Mamluk_Sultanate
Unpredictable phenomenon in complex systems
science due to a failure to demarcate weak and strong emergence, which are "quite different concepts". Both "weak" and "strong" positions hold that emergent
Emergence
Holomorphic functions in infinite dimensions
Gateaux holomorphy is the direct generalization of weak holomorphy to the fully infinite dimensional setting. Let X and Y be locally convex topological
Infinite-dimensional holomorphy
Infinite-dimensional_holomorphy
dimension of a module may refer to almost any of the various other dimensions, such as weak dimension, injective dimension, or projective dimension.
Glossary of commutative algebra
Glossary_of_commutative_algebra
Mathematical ranking of a set
weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders
Weak_ordering
Equations of motion for viscous fluids
time. It is studied in three spatial dimensions and one time dimension, and higher-dimensional analogues are studied in both pure and applied mathematics
Navier–Stokes_equations
Scientific law regarding conservation of a physical property
(violated by the weak interaction) Conservation of strangeness (violated by the weak interaction) Conservation of space-parity (violated by the weak interaction)
Conservation_law
French mathematician (1904–2008)
introduced fundamental concepts, including those of projective module, weak dimension, and what is now called the Cartan–Eilenberg resolution. Among his other
Henri_Cartan
Tabular arrangement of the chemical elements
uber eine neue Bestimmung des elektrischen Elementarquantums und der dimension des wasserstoffatoms. Sitzungsberichte der kaiserlichen Akademie der Wissenschaften
Periodic_table
3-category also called a Gray category, a weak 3-category. The coherence theorem of Gordon–Power–Street says a weak 3-category is equivalent (in some sense)
3-category
Country in Central Europe
original synthesis of architectural styles. By applying them to three-dimensional architectural elements, he produced a version of Art Nouveau that was
Hungary
Boson with spin 1
1980s, intermediate vector bosons (the W and Z bosons, which mediate the weak interaction) drew much attention in particle physics. A pseudovector boson
Vector_boson
Totality of psychological phenomena
mind, spirit, heart, and self as interconnected aspects of the spiritual dimension of humans. Daoism and Confucianism use the concept of heart-mind as the
Mind
Video game genre
Kangaroo (1982), while the Sega arcade game Congo Bongo (1983) adds a third dimension via isometric graphics. Another popular game of that period, Pitfall!
Platformer
Influence that can change motion of an object
electromagnetic, weak, and gravitational. High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic
Force
Perception of other people and of social situations
"strong-weak" dimension, an "active-passive" dimension, an "attractive-unattractive" dimension, etc. However, the evaluative "good-bad" dimension was the
Social_perception
Theorem in complex analysis
determination of bounds for the errors in such approximations. In a simple two-dimensional case, consider a function of two variables u(x,y) such that ∂ 2 u ∂ x
Maximum_principle
Gravitational deflection of light
distribution of mass. Because the third dimension involves not only distance but cosmic time, tomographic weak lensing is sensitive not only to the matter
Weak_gravitational_lensing
Problem in combinatorial optimization
that the sum of weights in each dimension d {\displaystyle d} does not exceed W d {\displaystyle W_{d}} . Multi-dimensional knapsack is computationally harder
Knapsack_problem
Theorem in differential topology
to Whitney). The weak Whitney embedding theorem states that any continuous function from an n-dimensional manifold to an m-dimensional manifold may be
Whitney_embedding_theorem
1994 book by Michio Kaku
Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension (1994, ISBN 0-19-286189-1) is a book by Michio Kaku, a theoretical physicist
Hyperspace_(book)
Quantum physical phenomenon
trajectory in low dimensions, the weak localization effect manifests itself much more strongly in low-dimensional systems (films and wires). In a system
Weak_localization
Fictional character
Seiya: Next Dimension, the canonical sequel to the original Saint Seiya manga, also written and illustrated by Masami Kurumada. In Next Dimension, Shun is
Andromeda_Shun
German philosopher (1844–1900)
his homosexual desire cannot simply be dismissed, "the evidence is very weak", and Köhler may be projecting twentieth-century understandings of sexuality
Friedrich_Nietzsche
Rings admitting weak inverses
is flat: this is also known as R being absolutely flat, or R having weak dimension 0 every short exact sequence of left R-modules is pure exact. The corresponding
Von_Neumann_regular_ring
Model of multi-species population dynamics
the attractor occur on a manifold of dimension N−1. This essentially says that the attractor cannot have dimension greater than N−1. This is important
Competitive Lotka–Volterra equations
Competitive_Lotka–Volterra_equations
2022 American film
External Dimension. However, none of this occurs within of a true reality: for them, the universe can be transmitted like a film to a Dimension beyond The
2025_Armageddon
European history from the 5th to 15th centuries
'fall' in the sense that the Western division of the Empire did. 2. The Dimension of Mediterannean Trade-In a famously controversial thesis, the medievalist
Middle_Ages
Enriched category Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory
Refinement_(category_theory)
Quotient space of a codomain of a linear map by the map's image
quotient space Y / im(f) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f. Cokernels are dual to the kernels
Cokernel
Upcoming video game
outside, but warm and hot inside, in the heart. He always wants to help the weak, although he himself only has limited days to live. We call this 'Xiake (侠客)'
Phantom_Blade_Zero
American heavy strategic bomber
election campaign in 1979, Ronald Reagan repeatedly stated that Carter was weak on defense and used the B-1 as a prime example. In response, on 22 August
Northrop_B-2_Spirit
English actor and filmmaker (1889–1977)
writes: "Henceforth, no movie fan would ever be able to separate the dimension of politics from [his] star image". Nevertheless, both Winston Churchill
Charlie_Chaplin
Bound on probability of a random variable being far from its mean
mean and variance are defined. For example, it can be used to prove the weak law of large numbers. Its practical usage is similar to the 68–95–99.7 rule
Chebyshev's_inequality
2025 Indian film by Kangana Ranaut
wrote, "Emergency is hindered by its overly dramatised approach and one-dimensional portrayals. The lack of narrative fluidity and context undermines the
Emergency_(2025_film)
Hypothetical invisible cosmic material
interacts via gravity and any other force (or forces) which is as weak as or weaker than the weak nuclear force, but also non-vanishing in strength. Many WIMP
Dark_matter
British stock market index
internationally focused companies: therefore the index's movements are a fairly weak indicator of how the UK economy is faring and are significantly affected
FTSE_100_Index
Paradigm in machine learning
Weak supervision (also known as semi-supervised learning) is a paradigm in machine learning, the relevance and notability of which increased with the advent
Weak_supervision
Controversies around the Nobel Prize in Physics
University of Manchester "for groundbreaking experiments regarding the two-dimensional material graphene". Several problems with the factual accuracy of the
Nobel Prize in Physics controversies
Nobel_Prize_in_Physics_controversies
2025 expansion of Destiny 2
Savathûn's Throne World). The affected destination has a red hue with dimensional tears in the sky, as well as a couple of other activities only available
Destiny_2:_Renegades
Mathematical construction used in homotopy theory
(abstract simplices) and maps between them. Simplicial sets are higher-dimensional generalizations of directed graphs. Every simplicial set gives rise to
Simplicial_set
Directive, as recital 16 states, "is based on the idea that the consumer is in a weak position vis-à-vis the seller or supplier, as regards both his bargaining
Law_of_the_European_Union
Number divisible only by 1 and itself
prime values. The Ulam spiral arranges the natural numbers in a two-dimensional grid, spiraling in concentric squares surrounding the origin with the
Prime_number
Category with direct sums and certain types of kernels and cokernels
spaces over a fixed field k is abelian, as is the category of finite-dimensional vector spaces over k. If X is a topological space, then the category
Abelian_category
Marvel Comics fictional character
humanoid Galan, who chooses to exile himself to an energy-rich alternate dimension before he can transform back into Galactus so that he can feed on that
Galactus
Class of drugs used to treat malignant tumors
The development of new antineoplastic drugs involves using the three-dimensional structure of targets, employing computer-aided drug design to rapidly
Antineoplastic
Japanese manga series by Yūji Iwahara
later revealed to be Shiro) who died while protecting Luna, though he is weaker in this form. His true form is a giant dark wolf with many tails. He is
Clevatess
Process of determining what a company will receive in exchange for its products
2014), MIT Technology Review Estelami, H: "Consumer Perceptions of Multi-Dimensional Prices", Advances in Consumer Research, 1997. "Chicago Cubs Host First
Pricing
2025 comic by Marvel Comics
the Dark Dimension and Invisible Woman punches him. Doom recovers the Eye of Agamotto and casts a spell to return Dormammu to the Dark Dimension. The next
One_World_Under_Doom
List of web series episodes
replacement for the TLC is a rather shoddy-looking structure, dubbed the Weak Trembling Fortress (WTF). Rocky is placed in the WTF. 8 "Meaty" Cary Huang
List of Battle for Dream Island episodes
List_of_Battle_for_Dream_Island_episodes
Relation between algebraic varieties and polynomial ideals
field (such as the complex numbers C {\displaystyle \mathbb {C} } ). The weak Nullstellensatz is a corollary (or a lemma, depending which is proved first)
Hilbert's_Nullstellensatz
Data, information, knowledge, wisdom hierarchy
hierarchical information paradigms have also been represented as two-dimensional charts, and as flow diagrams, where relationships between the components
DIKW_pyramid
Theory of subatomic structure
of nature: electromagnetism, the strong and weak nuclear forces, and gravity. Interest in eleven-dimensional supergravity soon waned as various flaws in
String_theory
Branch of mathematics
highly irregular, for example a fractal in the sense that its Hausdorff dimension is not an integer. This occurs even for mappings as simple as f ( z )
Complex_dynamics
1939 diplomatic crisis between Poland and Nazi Germany
(February 1984). "The French Government and the Danzig Crisis: The Italian Dimension". The International History Review. 6 (1): 48–87. doi:10.1080/07075332
Danzig_crisis
an n-group, or n-dimensional higher group, is a special kind of n-category that generalises the concept of group to higher-dimensional algebra. Here, n
N-group_(category_theory)
Legal concept regulating rights of a creative work
the Copyright Clause as the "Progress Clause" to emphasize the social dimension of intellectual property rights. The original length of copyright in the
Copyright
All bases of a vector space have equally many elements
In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may
Dimension theorem for vector spaces
Dimension_theorem_for_vector_spaces
Possible form of a matrix
the diagonal is in row echelon form, and a matrix in row echelon form is (weakly) upper triangular. Thus, the row echelon form can be viewed as a generalization
Row_echelon_form
Riemannian manifold with SU(n) holonomy
dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their
Calabi–Yau_manifold
Cryptographic algorithm
ISBN 978-0-471-12845-8. Meyer, Carl H.; Matyas, Stephen M. (1982). Cryptography: A New Dimension in Computer Data Security. John Wiley & Sons, Inc. pp. 77–85. ISBN 978-0-471-04892-3
Ciphertext_stealing
Tenth season of the ''Pokémon'' animated television series
September 28, 2006 (2006-09-28) – October 25, 2007 (2007-10-25) Season chronology ← Previous Battle Frontier Next → DP: Battle Dimension List of episodes
Pokémon the Series: Diamond and Pearl
Pokémon_the_Series:_Diamond_and_Pearl
Absence of diffusion waves in disordered media
lower critical dimension of the localization problem, the 2D case is in a sense close to 3D: states are only marginally localized for weak disorder and
Anderson_localization
Theory in particle physics
in a higher dimensional space. It is then suggested that the other forces of nature (the electromagnetic force, strong interaction, and weak interaction)
Large_extra_dimensions
Hypothetical black holes of very small size
holes would instantly evaporate, either totally or leaving only a very weakly interacting residue. Beside the theoretical arguments, cosmic rays hitting
Micro_black_hole
Fictional mutant superhero in Marvel Comics
in the "Age of Apocalypse" storyline. He is the biological son of his dimension's Scott Summers and Jean Grey, born of genetic tampering by Mr. Sinister
Nate_Grey
the Brain spawn and their space station, the Infosphere, into another dimension with a bomb given to him by the Nibblonians. The Cookieville Minimum-Security
List_of_Futurama_characters
monoidal tricategory is a one-object tetracategory in the sense of Trimble. Weak n-category infinity category Crans 2000. Hoffnung 2011. Crans, S. (2000)
Tetracategory
Stochastic process generalizing Brownian motion
\log(1/\varepsilon )}}}=1,\qquad {\text{almost surely}}.} The dimension doubling theorems say that the Hausdorff dimension of a set under a Brownian motion doubles almost
Wiener_process
Boundary condition for generalized functions
equations with prescribed boundary conditions (boundary value problems), where weak solutions may not be regular enough to satisfy the boundary conditions in
Trace_operator
Subphylum of arthropods
PMID 19104044 Garwood, Russell J.; Dunlop, Jason A. (2014). "Three-dimensional reconstruction and the phylogeny of extinct chelicerate orders". PeerJ
Chelicerata
1982 US science fiction film by Nicholas Meyer
matched. Spock notes that Khan's tactics indicate inexperience in three-dimensional combat, which Kirk exploits to disable Reliant. Mortally wounded, Khan
Star Trek II: The Wrath of Khan
Star_Trek_II:_The_Wrath_of_Khan
American investment management company
managed the public offering suggested that Bogle cancel the fund due to the weak reception, but Bogle refused. At this time, Vanguard had only three employees:
The_Vanguard_Group
Franco-Belgian comic book series
evolves: poetry and mystery of the little folk in the first, political dimension and social critique in the second, the fantastic and horror in the third
La_Légende_du_Changeling
Game theory concept
Haimanko and Zapecheinyuk (2006) studied one-dimensional AGs with weak strategic substitutes or weak strategic complements. They proved that all these
Aggregative_game
Phyllosilicate mineral in the pyrophyllite-talc group
cleavage and an uneven flat fracture, and it is foliated with a two-dimensional platy form. The Mohs scale of mineral hardness, based on scratch hardness
Talc
Semiaquatic rodent
The cerebellum is large, allowing the animal to move within a three-dimensional space (such as underwater) similar to tree-climbing squirrels. The neocortex
Beaver
Wayback Machine Salon, 5 April 2001. Quote: "Here we get to a further dimension of the difference between the two trades. Slavery in the West...the concept
History_of_slavery
Type of field-effect transistor
used as a turned-off switch, there is a weak-inversion current, sometimes called subthreshold leakage. In weak inversion where the source is tied to bulk
MOSFET
Study of human activity based on materials left behind
D. B.; Damrosch, D. R.; Pryor, J. & Thunen, R. L. (1985). "The Third Dimension in Site Structure: An Experiment in Trampling and Vertical Dispersal"
Archaeology
Role-playing video game series
rediscovered as the Serpent Isle, which had been moved to a different dimension or plane, so it seems likely that the other two continents still exist
Ultima_(series)
modacrylic is a synthetic copolymer. They are soft, strong, resilient, and dimensionally stable. Commercial production of modacrylic fiber began in 1949 by Union
Timeline of United States inventions (1946–1991)
Timeline_of_United_States_inventions_(1946–1991)
Scientific study of matter's behavior and properties
most familiar phases deal with three-dimensional systems, it is also possible to define analogs in two-dimensional systems, which has received attention
Chemistry
; Cunningham, Perry H.; Pitcher, Brian L. (1998), "The Consequential Dimension of Mormon Religiosity: A Conceptual Model with an Empirical Test", in
Demographics of the Church of Jesus Christ of Latter-day Saints
Demographics_of_the_Church_of_Jesus_Christ_of_Latter-day_Saints
Marvel Comics character
killing blow, Wolverine has Cloak teleport Romulus to the Dark Force dimension. Logan thinks about simply cutting his head as he did with Sabretooth
Daken
2011 science fiction novel by Ernest Cline
book gets off to a witty start" but noted that it lacks at least one dimension, stating that gaming had overwhelmed everything else about this book.
Ready_Player_One
Generalized function whose value is zero everywhere except at zero
mathematics, the delta function is often manipulated as a kind of limit (a weak limit) of a sequence of functions, each member of which has a tall spike
Dirac_delta_function
Combined military forces of India
combat arms, including artillery officers, to form a composite third-dimensional force for an integrated battle. IAF operates and flies attack Helicopters
Indian_Armed_Forces
Soviet penal labor camp system
13, 2011. Robert Conquest. "Knowing the Soviet Union: The Historical Dimension" (PDF). Archived from the original (PDF) on October 18, 2012. Retrieved
Gulag
{\displaystyle c(x,\eta )} , where Z d {\displaystyle Z^{d}} is a d-dimensional integer lattice, and c ( {\displaystyle c(} •,• ) {\displaystyle )} is
Voter_model
there motionless, and Bù Huàn activates it, allowing Yún Xiāo to fire at its weak point. Yún Xiāo misses twice, though, so Bù Huàn takes matters into his own
List of Thunderbolt Fantasy episodes
List_of_Thunderbolt_Fantasy_episodes
travel, tourism, insurance
WEAK DIMENSION
WEAK DIMENSION
Surname or Lastname
English
English : variant of Wick, specifically a habitational name from any of various places called Week or Weeke, notably in Cornwall, Hampshire, and Somerset.Americanized spelling of Norwegian or Swedish Vik.
Boy/Male
Arabic, Muslim
Weak
Boy/Male
Hindu
Peak
Surname or Lastname
English
English : topographic name for someone living by a pointed hill (or regional name from the Peak District (Old English Pēaclond) in Derbyshire), named with Old English pēac ‘peak’, ‘pointed hill’ (found only in place names). This word is not directly related to Old English pīc ‘point’, ‘pointed hill’, which yielded Pike; there is, however, some evidence of confusion between the two surnames.Possibly also Irish : reduced form of McPeak.Major concentrations of the surname Peak are found in Staffordshire and the West Country of England. Among the earliest known bearers are Richard del Pech or del Pek (d. 1196), son of Rannulf, sheriff of Nottingham, and Willielmus Piec (Winchester 1194). A century later, c.1284, a certain Richard del Peke settled in Denbighshire (now part of Clwyd), Wales, receiving lands from Henry de Lacey, earl of Lincoln, in return for helping to control the region. His descendants, who bear the name Peak(e), can be traced to the present day, and are found in New Zealand and Canada as well as in Britain. Peake is also the name of a family descended from John Pyke, who paid rent to the abbot of Leicester in 1477. The name took various forms, such as Peke and Pick, eventually becoming established as Peak in the 17th century.
Girl/Female
Australian, Christian, French, German, Hebrew
Hair; Lovelorn; Delicate; Weak
Surname or Lastname
English (Northumbria)
English (Northumbria) : topographic name for someone who lived by the Wear river in northern England. The river name is ancient, occuring in the form Vedra in Ptolemy’s Geographia; it is probably a Celtic word meaning ‘water’.English (Northumbria) : topographic name for someone who lived near a dam or weir, a variant spelling of Ware 1, or a habitational name from a place called Weare, in Devon and Somerset, from Old English wær, wer ‘weir’.
Girl/Female
Indian
Peak
Boy/Male
Arabic
One who has Weak Eyes
Girl/Female
Tamil
Peak
Boy/Male
Arabic, Muslim
Weak
Girl/Female
Hindu, Indian, Traditional
Peak
Boy/Male
Australian, Hindu, Indian
Peak
Biblical
weak; slacked
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Peak
Surname or Lastname
English
English : variant of Week.
Boy/Male
Tamil
Peak
Boy/Male
Hindu, Indian
Week
Surname or Lastname
English
English : variant spelling of Leake.
Boy/Male
Biblical
Weak, slacked.
Boy/Male
Spanish
Weak.
WEAK DIMENSION
WEAK DIMENSION
WEAK DIMENSION
WEAK DIMENSION
WEAK DIMENSION
WEAK DIMENSION
WEAK DIMENSION
v. i.
Wanting in power to influence or bind; as, weak ties; a weak sense of honor of duty.
v. i.
Not having power to convince; not supported by force of reason or truth; unsustained; as, a weak argument or case.
a.
To make or become weak; to weaken.
v. i.
Lacking ability for an appropriate function or office; as, weak eyes; a weak stomach; a weak magistrate; a weak regiment, or army.
v. i.
Lacking in elements of political strength; not wielding or having authority or energy; deficient in the resources that are essential to a ruler or nation; as, a weak monarch; a weak government or state.
v. i.
Tending towards lower prices; as, a weak market.
v. i.
Not able to sustain a great weight, pressure, or strain; as, a weak timber; a weak rope.
v. i.
Feeble of mind; wanting discernment; lacking vigor; spiritless; as, a weak king or magistrate.
v. i.
Not able to resist external force or onset; easily subdued or overcome; as, a weak barrier; as, a weak fortress.
v. i.
Wanting in point or vigor of expression; as, a weak sentence; a weak style.
v. i.
To rise or extend into a peak or point; to form, or appear as, a peak.
v. i.
Not able to withstand temptation, urgency, persuasion, etc.; easily impressed, moved, or overcome; accessible; vulnerable; as, weak resolutions; weak virtue.
n.
The upper aftermost corner of a fore-and-aft sail; -- used in many combinations; as, peak-halyards, peak-brails, etc.
a.
Having weak knees; hence, easily yielding; wanting resolution.
v. i.
Not firmly united or adhesive; easily broken or separated into pieces; not compact; as, a weak ship.
v. t.
To cause or make by friction or wasting; as, to wear a channel; to wear a hole.
a.
Having a weak mind, either naturally or by reason of disease; feebleminded; foolish; idiotic.
v. i.
Not stiff; pliant; frail; soft; as, the weak stalk of a plant.
v. i.
Not thoroughly or abundantly impregnated with the usual or required ingredients, or with stimulating and nourishing substances; of less than the usual strength; as, weak tea, broth, or liquor; a weak decoction or solution; a weak dose of medicine.
v.
A crack, crevice, fissure, or hole which admits water or other fluid, or lets it escape; as, a leak in a roof; a leak in a boat; a leak in a gas pipe.
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