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mathematics, the dual module of a left (respectively right) module M over a ring R is the set of left (respectively right) R-module homomorphisms from
Dual_module
In abstract algebra, a dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle
Dualizing_module
Computer memory module
A DIMM (Dual In-line Memory Module) is a type of memory module used in computers. It is a printed circuit board with one or both sides (front and back)
DIMM
Operation that pairs a left and a right R-module into an abelian group
extend to modules. Yet, some useful properties of the tensor product, considered as module homomorphisms, remain. The dual module of a right R-module E, is
Tensor_product_of_modules
Replaceable RAM form factor
memory modules. SO-DIMMs were developed in 1997 as a size-reduced version of the Dual In-line Memory Module (DIMM). Both are removable memory modules that
CAMM_(memory_module)
General concept and operation in mathematics
Dual system Duality (electrical engineering) Duality (optimization) Duality (projective geometry) Dualizing module Dualizing sheaf Koszul duality Langlands
Duality_(mathematics)
Theorem in algebra
In algebra, Matlis duality is a duality between Artinian and Noetherian modules over a complete Noetherian local ring. In the special case when the local
Matlis_duality
Printed circuit board for computer memory
Memory Module SIMM, a single in-line memory module DIMM, dual in-line memory module Rambus memory modules are a subset of DIMMs, but are normally referred
Memory_module
{\displaystyle a\mapsto a.x-x.a} for some x {\displaystyle x} in the dual module). An equivalent characterization is that A is amenable if and only if it
Amenable_Banach_algebra
Type of random-access memory for computers
the module includes non-volatile memory, backup power is required for only a short time after the computer's main power fails, while the module copies
NVDIMM
Generalization of vector spaces from fields to rings
R-modules preserves exactness. Torsionless A module is called torsionless if it embeds into its algebraic dual. Simple A simple module S is a module that
Module_(mathematics)
Technology company
they launched their first single-module microinverter, the YC200. In 2012, APS launched its flagship YC500 dual-module microinverter and planned the YC1000-3
APsystems
Sheaf consisting of modules on a ringed space; generalizing vector bundles
O-modules, then ℋomO(F,G) denotes the O-module that is the sheaf U↦HomO|U(F|U,G|U). In particular, the O-module ℋomO(F,O) is called the dual module of
Sheaf_of_modules
Mathematical object in abstract algebra
homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in (Baer 1940) and are discussed
Injective_module
In mathematics, vector space of linear forms
contravariance of vectors Dual module Dual norm Duality (mathematics) Duality (projective geometry) Pontryagin duality Reciprocal lattice – dual space basis, in
Dual_space
algebra, Grothendieck local duality is a duality theorem for cohomology of modules over local rings, analogous to Serre duality of coherent sheaves. Suppose
Grothendieck_local_duality
for rings. In many ways, it is the dual notion to that of the socle soc(M) of M. Let R be a ring and M a left R-module. A submodule N of M is called maximal
Radical_of_a_module
Module over a sheaf of differential operators
In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of
D-module
Operation in abstract algebra
dual notion. The most familiar examples of this construction occur when considering vector spaces (modules over a field) and abelian groups (modules over
Direct_sum_of_modules
Computer memory architecture
to install memory for that particular unit. For dual-channel use, the matched pair of memory modules may usually be placed in the first bank of each channel
Multi-channel memory architecture
Multi-channel_memory_architecture
Low-cost, low-power SoC microcontrollers with Bluetooth and Wi-Fi
Tensilica Xtensa LX6 microprocessor available in dual-core and single-core variants, the Xtensa LX7 dual-core processor, or a RISC-V microprocessor. The
ESP32
right Ore u.dim(DD) = 1 u.dim(DD) < ∞ The dual notion of a uniform module is that of a hollow module: a module M is said to be hollow if, when N1 and N2
Uniform_module
neither zero nor an isomorphism. dual module The dual module of a module M over a commutative ring R is the module Hom R ( M , R ) {\displaystyle \operatorname
Glossary_of_module_theory
Linear map over a ring
_{R}(M,R)} is called the dual module of M; it is a left (resp. right) module if M is a right (resp. left) module over R with the module structure coming from
Module_homomorphism
Optical transceiver that uses coherent modulation
FlexE. The initial ACO IA is for the CFP2 module. The typical optical modulations that are used include Dual Polarization Quadrature Phase Shift Keying
Coherent_optical_module
Computer memory module
one or both sides. It differs from a dual in-line memory module (DIMM), the most predominant form of memory module since the late 1990s, in that the contacts
SIMM
Ring that is also a vector space or a module
commutative ring R. Since A is in particular a module, we can take the dual module A* of A. A priori, the dual A* need not have a structure of an associative
Associative_algebra
Guidance and navigation computer used in Apollo spacecraft
program that was installed on board each Apollo command module (CM) and Apollo Lunar Module (LM). The AGC provided computation and electronic interfaces
Apollo_Guidance_Computer
Real numbers adjoined with a nil-squaring element
general construction of the dual numbers. Given a commutative ring R and a module M, there is a ring R[M] called the ring of dual numbers which has the following
Dual_number
Planned commercial space station
with a large robotic arm for servicing cargo and external payloads The dual-module station is intended to be launched in a single launch, no earlier than
Starlab_(space_station)
Various mathematical dualites
})^{*}} . An extension of Koszul duality to D-modules states a similar equivalence of derived categories between dg-modules over the dg-algebra Ω X {\displaystyle
Koszul_duality
generated modules over Λ to modules over the opposite algebra Λop. If M is a left Λ-module then the right Λ-module M* is defined to be HomΛ(M,Λ). The dual D(M)
Artin_algebra
Optical transceiver used in high-bandwidth data communications
CFP2 module. The typical optical modulation that are used include Dual Polarization Quadrature Phase Shift Keying (DP-QPSK) and QAM-16. These modules put
Optical_module
notion was introduced by Hyman Bass. A module is torsionless if and only if the canonical map into its double dual, M → M ∗ ∗ = Hom R ( M ∗ , R ) , m
Torsionless_module
Synthesizer introduced in the 1980s
modular synthesizer modules based on the original Roland System-100M modules: 110 VCO/VCF/VCA 112 Dual VCO 121 Dual VCF 130 Dual VCA 140 Dual Envelope/LFO 150
Roland_System-100M
Scalar-valued bilinear function
referred to as the split-case. Given a ring R and a right R-module M and its dual module M∗, a mapping B : M∗ × M → R is called a bilinear form if B(u
Bilinear_form
Type of synchronous dynamic random-access memory
32-bit modules provide two channels. Therefore, a dual-channel mainboard accepting 16-bit modules must have RIMMs added or removed in pairs. A dual-channel
RDRAM
Proprietary software with time-limited free use
cardware. "Empathy" is a postcardware for password-protected executables. Dual Module Player and Linux were also postcardware for a long time. An example of
Shareware
corepresentation is a concept dual to a module. The definition of a comodule over a coalgebra is formed by dualizing the definition of a module over an associative
Comodule
Equivalence relation on rings
equivalence and a similar notion of duality in 1958. Rings are commonly studied in terms of their modules, as modules can be viewed as representations of
Morita_equivalence
Microcontroller peripheral interface
(peripheral module interface) is an open standard defined by Digilent in the Pmod Interface Specification for connecting peripheral modules to FPGA and
Pmod_Interface
(which amounts to gluing modules of Kähler differentials on affine charts to get the globally defined cotangent sheaf). The dual module of the cotangent sheaf
Cotangent_sheaf
Duality for Galois modules for the absolute Galois group of a non-archimedean local field
In Galois cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean
Local_Tate_duality
Map from a vector space to its underlying field
a free module over a commutative ring A. We view A as a free module of rank 1 over itself. By the dual module Ev of E we shall mean the module Hom(E,
Functional_(mathematics)
Linear algebra concept
introduce the dual space of a vector space (module) is by introducing it in a categorical sense. To do this, let A {\displaystyle A} be a module defined over
Dual_basis
In algebra, module with a finite generating set
generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over
Finitely_generated_module
4th generation of the mainline series of Raspberry Pi single-board computer
Compute Module 4, the MSRP ranges from $30 to $95 depending on the configuration. It is offered in two formats: the Compute Module 4 with dual 100-pin
Raspberry_Pi_4
A. dual duality dualizing 1. Grothendieck local duality is a duality for cohomology of modules over a local ring. 2. Matlis duality is a duality between
Glossary of commutative algebra
Glossary_of_commutative_algebra
Computer memory chips used as a set
pages. Multi-rank modules have higher loading on the data bus (and on unbuffered DIMMs the CA bus as well). Therefore if more than dual rank DIMMs are connected
Memory_rank
Device which reduces humidity
Andrew J.; Oh, Jinwoo; Braun, James E.; Warsinger, David M. (2024). "Dual-module humidity pump for efficient air dehumidification: Demonstration and performance
Dehumidifier
Bilinear map in mathematics
pairing k 2 × k 2 → k {\displaystyle k^{2}\times k^{2}\to k} . For the dual module M ∗ {\displaystyle M^{*}} of M {\displaystyle M} , the evaluation map
Pairing
Line of gamepads developed by Sony
The DualShock (originally Dual Shock, trademarked as DUALSHOCK or DUAL SHOCK, with the PlayStation 5 version as DualSense) is a line of gamepads developed
DualShock
Field theory involving topological effects in physics
Z(Σ)* where Σ* is Σ with opposite orientation and Z(Σ)* denotes the dual module, Z is multiplicative. Z( ∅ {\displaystyle \emptyset } ) = Λ for the d-dimensional
Topological quantum field theory
Topological_quantum_field_theory
Duality for locally compact abelian groups
left R–module, the dual group G^ will become a right R–module; in this way we can also see that discrete left R–modules will be Pontryagin dual to compact
Pontryagin_duality
Modular synthesizer, introduced the Eurorack standard
stage vactrol phaser A-101-6 – Six Stage Opto FET VCF A-101-9 – Dual universal vactrol module A-102 – EMS VCS 3 style 18 dB/octave diode low-pass filter A-103
Doepfer_A-100
Type of computer memory
rates than those for which it was made. DDR SDRAM modules for desktop computers, dual in-line memory modules (DIMMs), have 184 pins (as opposed to 168 pins
DDR_SDRAM
Nvidia's line of general purpose GPUs
VizWorld.com. Retrieved 11 December 2015. "Tesla M2090 Dual-Slot Computing Processor Module" (PDF). Nvidia.com. Retrieved 11 December 2015. "Tesla K10
Nvidia_Tesla
Exact sequence used to describe the structure of an object
algebra, a resolution (or left resolution; dually a coresolution or right resolution) is an exact sequence of modules (or, more generally, of objects of an
Resolution_(algebra)
Analogue modular synthesizer
panel for power distribution. The first generation of modules consisted of: Dual voltage processor Dual audio mixer Peak and trough Triple bidirectional router
Serge_synthesizer
In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic
Tate_duality
Virtual reality headset
rendering. The front portion of the strap contains the facial interface, dual speakers, and the microSD card slot, while the back portion features a USB-C
Steam_Frame
Soviet/Russian space station (1986–2001)
left without Soyuz spacecraft or modules to launch to the station at first. It was decided to launch Soyuz T-15 on a dual mission to both Mir and Salyut
Mir
Direct summand of a free module (mathematics)
projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring, keeping some of the main properties of free modules. Various
Projective_module
Dual pair of vector spaces
In mathematics, a dual system, dual pair or a duality over a field 𝕂 is a triple (X,Y,b) consisting of two vector spaces, X and Y, over 𝕂 and a non-degenerate
Dual_system
Algebraic structure
used in Wiles's proof of Fermat's Last Theorem): Duality (mathematics), Eben Matlis; Dualizing module, Popescu's theorem, Artin approximation theorem.
Commutative_ring
org C.S0065 Qualcomm TIA Standardizes Removable User Identity Modules Why do CDMA Subscribers Need the R-UIM? – PDF whitepaper Dual-mode R-UIM v t e
Removable User Identity Module
Removable_User_Identity_Module
1999 American crewed spaceflight to the ISS
International Space Station carrying the Spacehab Double Module (DM) 13th Spacehab overall (6th dual module use). Space Shuttle Discovery carried to the ISS an
STS-96
A module M is dualizable if and only if it is a finitely generated projective module. In that case the dual object M∗ is also given by the module of
Dual_object
1983 adventure module for the Dungeons & Dragons game
Ravenloft is an adventure module for the Dungeons & Dragons (D&D) fantasy role-playing game. The American game publishing company TSR, Inc. released it
Ravenloft_(module)
phase". Archived from the original on 2018-01-21. "EcoMotors opoc™ Dual-Module | EcoMotors". Archived from the original on 2013-05-01. Retrieved 2013-05-06
EcoMotors
System-on-a-chip microcontroller model with Wi-Fi
9 DIL", meaning two rows of 9 pins arranged "Dual In Line", like the pins of DIP ICs. Many ESP-xx modules include a small onboard LED which can be programmed
ESP8266
Duality for sheaves of k-modules over a locally compact space
mathematics, Verdier duality is a cohomological duality in algebraic topology that generalizes Poincaré duality for manifolds. Verdier duality was introduced
Verdier_duality
Linear map from a vector space to its field of scalars
The existence of "enough" linear forms on a module is equivalent to projectivity. Dual Basis Lemma—An R-module M is projective if and only if there exists
Linear_form
Programmable SIM card embedded into a device
An eSIM (embedded subscriber identity module) is a form of SIM card that is embedded directly into a device as software installed onto an eUICC chip. In
ESIM
Index of articles associated with the same name
of M {\displaystyle M} . It can be considered as a dual notion to that of the radical of a module. In set notation, s o c ( M ) = ∑ N is a simple submodule
Socle_(mathematics)
Concept in mathematics
every module can be mapped via a monomorphism whose image is essential in an injective module (its injective hull), one might ask if the dual statement
Essential_extension
Empirical study of systems in transformation
triangles of the spherical icosahedron. (See Sec. 1043.00.) The A and B Quanta Modules. Omnirationality: the identification of triangling and tetrahedroning with
Synergetics_(Fuller)
Type of vehicle transmission
A dual-clutch transmission (DCT) (sometimes referred to as a twin-clutch transmission) is a type of multi-speed vehicle transmission system, that uses
Dual-clutch_transmission
Modular monophonic analog synthesizer
with a dual core design, resulting in good tuning stability compared to competitors. The sliding matrix switches found above and below the modules and are
ARP_2500
Mathematical theorem in representation theory
Schur–Weyl duality is the statement that the space of two-tensors decomposes into symmetric and antisymmetric parts, each of which is an irreducible module for
Schur–Weyl_duality
Israeli hardware developer
components, mainly mini computers, Single-board computers, System-on-module, computer-on-module, Edge servers and Industrial PCs devices. It provides OEMs powerful
SolidRun
processing and for Multi-Processing Modules (MPM) which dispatches data processing to threads or processes. Many additional modules (or "mods") are available to
List_of_Apache_modules
M_{P}\cong R_{P}} for all primes P of R. Now, if M is an invertible R-module, then its dual M* = Hom(M,R) is its inverse with respect to the tensor product
Invertible_module
Technology that can be used for both peaceful and military purposes
In politics, diplomacy and export control, dual-use items refer to equipment, machines, goods and technology (both hardware and software) that can be used
Dual-use_technology
switch offering, 12-module slot chassis with dual fabric modules and options for dual management modules and system support modules for high availability
List_of_ProCurve_products
Generalization of a rectangle for higher dimensions
in database theory or ranges of integers, rather than real numbers. The dual polytope of an n-orthotope has been variously called a rectangular n-orthoplex
Hyperrectangle
Server and workstation processor line by AMD
dual-processor configurations Socket C32 Released November 14, 2011. CPU steppings: B2 Multi-chip module consisting of two dies, each with one dual-core
Opteron
Integrated circuit card for mobile devices
A SIM card or SIM (subscriber identity module) is a type of integrated circuit, often in the form of a smart card. They are intended to securely store
SIM_card
Microprocessor with more than one processing unit
referred to by another name, such as multi-chip module. This article uses the terms "multi-core" and "dual-core" for CPUs manufactured on the same integrated
Multi-core_processor
Concept from algebraic geometry
to construct the dualizing sheaf on X. coherent duality reflexive sheaf Gorenstein ring Dualizing module Hartshorne 1977, Ch. III, § 7. Kollár & Mori 1998
Dualizing_sheaf
Type of computer memory
same 14 ns latency as DDR4 and DDR3. DDR5 octuples the maximum dual in-line memory module (DIMM) capacity from 64 GB to 512 GB. DDR5 also has higher frequencies
DDR5_SDRAM
Mobile phone with two SIM cards
SIM. Dual mode mobile Subscriber Identity Module SIM cloning Shanzhai Sin, Ben (August 2, 2018). "The Dual Sim iPhone Is What Many In Asia And Europe
Dual_SIM
Microarchitecture by AMD
CMT module is equal to a dual-core processor in its integer calculation capabilities, and to either a single-core processor or a handicapped dual-core
Bulldozer_(microarchitecture)
Hypothetical concept in neuroscience
Dual consciousness (also known as dual mind or divided consciousness) is a hypothesis in neuroscience. It is proposed that it is possible that a person
Dual_consciousness
Processor family
mainstream 64-bit x86-64 single-, dual-, and quad-core microprocessors based on the Core microarchitecture. The single- and dual-core models are single-die,
Intel_Core_2
Type of computer memory introduced 2014
of 30 nm modules. In July, Samsung announced that it would begin sampling the industry's first 16 GB registered dual inline memory modules (RDIMMs) using
DDR4_SDRAM
Two fundamental and often opposing concepts
Dualism or dualistic cosmology is the belief that two fundamental concepts exist, which often oppose each other. It is an umbrella term that covers a
Dualism_in_cosmology
Vehicle safety device
It consists of an airbag cushion, a flexible fabric bag, an inflation module, and an impact sensor. The purpose of the airbag is to provide a vehicle
Airbag
Saturn V-launched payload that took men to the Moon
spacecraft consisted of a combined command and service module (CSM) and an Apollo Lunar Module (LM). Two additional components complemented the spacecraft
Apollo_(spacecraft)
Modular handheld computer
handheld computer made by ClockworkPi, designed as an enclosure for compute modules such as the Raspberry Pi. It is sold as a kit and aimed at computer hobbyists
UConsole
travel, tourism, insurance
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travel, tourism, insurance