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In mathematics, a binomial ring is a commutative ring whose additive group is torsion-free and contains all binomial coefficients ( x n ) = x ( x − 1 )
Binomial_ring
Algebraic expansion of powers of a binomial
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem
Binomial_theorem
Number of subsets of a given size
mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is
Binomial_coefficient
generally, any binomial ring becomes a λ-ring if we define the λ-operations to be the binomial coefficients, λn(x) = (x n). In these λ-rings, all Adams operations
Λ-ring
Mathematical fallacy
prime. Since a binomial coefficient is always an integer, the nth binomial coefficient is divisible by p and hence equal to 0 in the ring. We are left with
Freshman's_dream
Algebraic structure with addition and multiplication
and is called the zero ring. If a ring R contains the zero ring as a subring, then R itself is the zero ring. The binomial formula holds for any x and
Ring_(mathematics)
Fixed phrase of two or more conventionally joined words
linguistics and stylistics, an irreversible binomial, frozen binomial, binomial freeze, binomial expression, binomial pair, or nonreversible word pair is a
Irreversible_binomial
Polynomial with integer values for integer inputs
MR 1918189. Zbl 1065.55003. Elliott, Jesse (2006). "Binomial rings, integer-valued polynomials, and λ-rings". Journal of Pure and Applied Algebra. 207 (1):
Integer-valued_polynomial
Reduction of a ring by one of its ideals
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite
Quotient_ring
Species of snake
Diadophis punctatus, commonly known as the ring-necked snake or ringneck snake, is a small, harmless species of colubrid snake found throughout much of
Ring-necked_snake
Species of mammal from Madagascar
The ring-tailed lemur (Lemur catta) is a medium- to larger-sized strepsirrhine (wet-nosed) primate and the most internationally recognized lemur species
Ring-tailed_lemur
Species of bird
The common pheasant (Phasianus colchicus), ring-necked pheasant, or blue-headed pheasant, is a bird in the pheasant family (Phasianidae). The genus name
Common_pheasant
Algebraic structure
ring R, there is a unique ring homomorphism Z → R. By means of this map, an integer n can be regarded as an element of R. For example, the binomial formula
Commutative_ring
Species of mammal
mammal of Arizona. The species is known by a variety of common names, such as ring-tailed cat, miner's cat, civet cat, and cacomistle (or cacomixtle), though
Ringtail
Species of carnivore
The ringed seal (Pusa hispida) is a small earless seal species found in Arctic and sub-Arctic regions. Its common name is derived from a distinctive patterning
Ringed_seal
Species of bird
The rose-ringed parakeet (Psittacula krameri), also known as the ring-necked parakeet, or colloquially as the Indian Ringneck, is a medium-sized parrot
Rose-ringed_parakeet
Infinite sum that is considered independently from any notion of convergence
series with coefficients in a ring R is called a formal power series over R. The formal power series over a ring R form a ring, commonly denoted by R[[x]]
Formal_power_series
American mathematician
degree in 1997 and completing her Ph.D. there in 2001. Her dissertation, Binomial Rings and Algebras, was supervised by Frank Wylie Anderson. She has been a
Jessica_Sklar
Ideal of the nilpotent elements
the ring, or equivalently the radical of the zero ideal. This is an ideal because the sum of any two nilpotent elements is nilpotent (by the binomial formula)
Nilradical_of_a_ring
Species of bird
The ring-necked dove (Streptopelia capicola), also known as the Cape turtle dove, half-collared dove, or the Cape Lager is a widespread and often abundant
Ring-necked_dove
Species of lizard
The ring-tailed gecko (Cyrtodactylus louisiadensis) is a species of gecko that is endemic to the Louisiade Archipelago of Papua New Guinea. Harlow, P.
Ring-tailed_gecko
Species of venomous cephalopod
The greater blue-ringed octopus (Hapalochlaena lunulata) is one of four species of extremely venomous blue-ringed octopuses belonging to the family Octopodidae
Greater_blue-ringed_octopus
Mathematical expression with disputed status
applies with R replaced by any ring. Defining 00 = 1 is necessary for many polynomial identities. For example, the binomial theorem (1+x)n=∑k=0n(nk)xk holds
Zero_to_the_power_of_zero
Monotypic cobra-like species of African elapid
(/ˈrɪŋk(h)æls/; Hemachatus haemachatus), also known as the ringhals /ˈrɪŋhæls/ or ring-necked spitting cobra, is a species of venomous snake in the family Elapidae
Rinkhals
Species of palm
fruit is notably used by indigenous Amazonians to make black rings. In the 1800s, this ring was used as a symbol of marriage for the slaves and natives
Astrocaryum_vulgare
Species of bird
The ring-necked francolin (Scleroptila streptophora) is a bird species in the family Phasianidae. It is found in Burundi, Cameroon, Kenya, Rwanda, Tanzania
Ring-necked_francolin
Species of bird
Aves Order: Columbiformes Family: Columbidae Genus: Streptopelia Species: S. decaocto Binomial name Streptopelia decaocto (Frivaldszky, 1838) Audio Song
Eurasian_collared_dove
Data about other data
data: UML, EDIFACT, XSD, Dewey/UDC/LoC, SKOS, ISO-25964, Pantone, Linnaean Binomial Nomenclature, etc. Using controlled vocabularies for the components of
Metadata
Generalization of the product rule in calculus
is given by (fg)(n)=∑k=0n(nk)f(n−k)g(k), where (nk)=n!k!(n−k)! is the binomial coefficient and f(j) denotes the j-th derivative of f (and in particular
General_Leibniz_rule
Theorem of matrix ranks
While the identity is primarily used on matrices, it holds in a general ring or in an Ab-category. The Woodbury matrix identity allows efficient computation
Woodbury_matrix_identity
Species of carnivore
The South American coati (Nasua nasua), also known as the ring-tailed coati or brown-nosed coati, is a coati species and a member of the raccoon family
South_American_coati
Species of centipede
common names, including the African giant centipede and the Tanzanian blue ring centipede. Ethmostigmus trigonopodus from northern parts of Nigeria can reach
Ethmostigmus_trigonopodus
Species of bird
The Barbary dove, ringed turtle dove, ringneck dove, ring-necked turtle dove, or ring dove (Streptopelia risoria) is a domestic member of the dove and
Barbary_dove
Species of flowering plant
Order: Piperales Family: Piperaceae Genus: Piper Species: P. sarmentosum Binomial name Piper sarmentosum Roxb. Synonyms List Chavica hainana C.DC. Chavica
Piper_sarmentosum
Species of fungus
Agaricales Family: Tricholomataceae Genus: Leucopaxillus Species: L. gentianeus Binomial name Leucopaxillus gentianeus (Quél.) Kotl. (1966) Synonyms Clitocybe gentianea
Leucopaxillus_gentianeus
Rank Common name Binomial Name Average mass kg (lb) 1 Aepyornis maximus 850 kg (1,870 lb) 2 Dromornis stirtoni 500 kg (1,100 lb) 3 Pachystruthio dmanisensis
Largest_prehistoric_animals
States of matter for water as a solid
are (42)=6 allowed configurations of hydrogens for this oxygen atom (see Binomial coefficient). Thus, there are 6N/2 configurations that satisfy these N/2
Phases_of_ice
Brackets as used in mathematical notation
Braces, as in {π} < 1/7, may denote the fractional part of a real number. Binomial coefficient Bracket polynomial Bra-ket notation Delimiter Dyck language
Bracket_(mathematics)
Species of fish
most likely to be Maka at the mouth of the Moa River in Sierra Leone. The binomial consists of the generic name which is a compound of the Greek words ἐπί
Clown_killi
Species of wasp
of the most intricate Mullerian mimicry rings in the natural world, being divided into eight separate rings of mimicry. Their behavior and coloring has
Dasymutilla_occidentalis
(with Gottfried Leibniz) of differential calculus. He also created the binomial theorem, worked extensively on optics, and created a law of cooling. Figures
Culture_of_the_United_Kingdom
Species of butterfly
yellow, four small indistinct spots along the outer margin, and a broad ring on the abdominal margin dull red; beneath the primaries are paler than demetrius
Papilio_macilentus
Species of owl
Naturae. He placed it with the other owls in the genus Strix and coined the binomial name Strix virginia. Gmelin based his description on that of English naturalist
Great_horned_owl
Species of butterfly
beneath united into hooks and the posterior ones into rings.Some males have above a red anal ring on the hindwing. In the female the forewing in the cell
Papilio_rumanzovia
Species of fish
Danio tinwini, commonly called gold-ring danio, is a newly discovered species of Danio from Myanmar. It is also referred to as Danio sp. "TW02". It is
Danio_tinwini
Species of fungus
sometimes called fairy ring mushroom since it often forms fairy rings. Fairy ring about 2 meters diameter, Queensland, Australia Fairy ring about 6 meters diameter
Chlorophyllum_molybdites
Species of lizard
Family: Varanidae Genus: Varanus Subgenus: Soterosaurus Species: V. salvator Binomial name Varanus salvator (Laurenti, 1768) Range of Asian water monitor subspecies:
Asian_water_monitor
Species of lovebird
(Agapornis personatus), also called masked lovebird, black-masked lovebird or eye ring lovebird, is a monotypic species of bird of the lovebird genus in the parrot
Yellow-collared_lovebird
Cat-like species of mammal from Madagascar
(Fossa) †C. spelea (giant cave fossa) Fossa (Malagasy civet) Eupleres Galidia (ring-tailed mongoose) Galidictis Salanoia Mungotictis (narrow-striped mongoose)
Fossa_(animal)
Species of owl
landmark 1758 10th edition of Systema Naturae, where it was given the binomial name Strix scandiaca. The genus name Bubo is Latin for "horned owl" and
Snowy_owl
Species of bird
The ring-billed gull (Larus delawarensis) is a medium-sized gull native to North America, breeding in Canada and the northern Contiguous United States
Ring-billed_gull
Species of fungus
Agaricus hondensis, commonly known as the felt-ringed agaricus, is a species of fungus in the family Agaricaceae. The species was officially described
Agaricus_hondensis
Element in a ring whose some power is 0
from a commutative ring R form an ideal 𝔑; this is a consequence of the binomial theorem. This ideal is the nilradical of the ring. If 𝔑={0}, i.e., R
Nilpotent
Species of tree
acetogenins from the seeds of Asimina triloba possessing a bis-tetrahydrofuran ring". Journal of Natural Products. 68 (2): 194–197. Bibcode:2005JNAtP..68..194K
Asimina_triloba
Species of fungus
type species that belonged to the Agaricaceae. It was given its current binomial name in 2001 as a result, as this and other species were moved to the new
Coprinopsis_atramentaria
Freshwater seal found in Finland
The Saimaa ringed seal (Pusa saimensis, Finnish: saimaannorppa, Swedish: saimenvikare) is a species of seal. It is among the most endangered seals in the
Saimaa_ringed_seal
Species of fungus
lamella (mushroom gills), and the mushroom stalk (stipe) has a annulus (ring). The mycelium invades the sapwood of trees, and is able to disseminate,
Armillaria_ostoyae
Species of fungus
Friedrich Müller in 1780 as Agaricus comatus, before being given its current binomial name in 1797 by Christiaan Hendrik Persoon. Its specific name derives from
Coprinus_comatus
Species of bird
The ringed warbling finch (Microspingus torquatus) is a species of bird in the family Thraupidae. It is endemic to Bolivia. Its natural habitats are subtropical
Ringed_warbling_finch
Species of plant endemic to New South Wales, Australia
Grey spider flower Grevillea buxifolia in Ku-ring-gai Chase National Park Conservation status Least Concern (IUCN 3.1) Scientific classification Kingdom:
Grevillea_buxifolia
Species of fish
Acanthochaetodon,. The specific name of this species, annularis, means "ringed" which refers to the ring on the body above the gill cover. Bluering angelfish are infrequently
Bluering_angelfish
Mathematical set of all subsets of a set
numbers, in which case we cannot enumerate all irrational numbers. The binomial theorem is closely related to the power set. A k–elements combination from
Power_set
Species of fungus
Binomial names may take the form "noun + adjective", "noun + nominative noun" or "noun + genitive noun" as explained in this section of the Binomial nomenclature
Agaricus_xanthodermus
Species of bird
specimen collected near Bordentown, New Jersey. Bonaparte later coined the binomial name, Falco cooperii. The specific epithet and the common name were chosen
Cooper's_hawk
Species of fungus
while when older, the cap is convex. The stipe has warts as well, has a ring, and is bulbous at the base. Length of the stipe is 9-12 cm. Gills have a
Saproamanita_foetidissima
Species of fungus
For many years Agaricus moelleri was erroneously accredited with the binomial Agaricus placomyces by some British authors. The epithet placomyces was
Agaricus_moelleri
Species of fish
The white-ring garden eel (Heteroconger canabus), also known as the Cape garden eel in Mexico, is an eel in the family Congridae (conger/garden eels).
White-ring_garden_eel
Species of lemur
sportive lemur (L. manasamody) Small-toothed sportive lemur (L. microdon) Ring sportive lemur (L. milanoii) Mittermeier's sportive lemur (L. mittermeieri)
Daraina_sportive_lemur
1 million insect species having been formally described and assigned a binomial name, insects are the most diverse group of animals, comprising approximately
List_of_insect_orders
Fossil flora and fauna of North American site
most diverse leaf quarry from the Hell Creek Formation. "TYPE" after the binomial means that it is represented by a type specimen found in the Yale-Peabody
Paleobiota of the Hell Creek Formation
Paleobiota_of_the_Hell_Creek_Formation
Species of mushroom
Order: Agaricales Family: Agaricaceae Genus: Calvatia Species: C. gigantea Binomial name Calvatia gigantea (Batsch ex Pers.) Lloyd Synonyms Langermannia gigantea
Calvatia_gigantea
Species of bird
where it lives alongside feral populations of its close relative, the rose-ringed parakeet (Psittacula krameri). The Alexandrine parakeet was first described
Alexandrine_parakeet
Species of butterfly
Ypthima baldus, the common five-ring, is a species of butterfly in the subfamily Satyrinae found in Asia. Male: Upperside brown, both forewing and hindwing
Ypthima_baldus
Species of bird
The ring-necked duck (Aythya collaris) is a diving duck from North America commonly found in freshwater ponds and lakes. The scientific name is derived
Ring-necked_duck
corresponding type specimens, type localities, and type repositories. Binomial names are listed alphabetically by specific epithet and presented in their
List of giant squid specimens and sightings
List_of_giant_squid_specimens_and_sightings
Domesticated species of canid
Retrieved 15 December 2020. VnExpress. "47 dogs seized as police bust dog meat ring in southern Vietnam - VnExpress International". VnExpress International –
Dog
Extremely venomous snake native to Australia
therefore, had priority and was adopted for the combined genus. The current binomial name of the inland taipan has therefore been Oxyuranus microlepidotus since
Inland_taipan
Mathematical set with repetitions allowed
"n choose k" for (nk). Like the binomial distribution that involves binomial coefficients, there is a negative binomial distribution in which the multiset
Multiset
David (1971). "Research Problems: How often does an integer occur as a binomial coefficient?". American Mathematical Monthly. 78 (4): 385–386. doi:10.2307/2316907
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Largest integer that divides given integers
Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below). The greatest common divisor (GCD) of integers a and
Greatest_common_divisor
Cryptographic protocol designed to resist quantum computer attacks
binomial distribution. Error Reconciliation: What distinguishes NewHope from its predecessors is its method for error reconciliation. Previous ring learning
NewHope
Species of fungus
species on well-drained soils. It is found solitary or in groups and fairy rings in pastures and occasionally in woodland. It is widespread in temperate
Macrolepiota_procera
Species of mollusc
The southern blue-ringed octopus (Hapalochlaena maculosa) is one of four extremely venomous species of blue-ringed octopuses. It is most commonly found
Southern_blue-ringed_octopus
One-humped camel
and the two-humped Bactrian camel. The dromedary was given its current binomial name Camelus dromedarius by Swedish zoologist Carl Linnaeus in his 1758
Dromedary
Species of fungus
Clitocybe species be split off into a new genus Infundibulicybe, thus the new binomial name is Infundibulicybe geotropa. A cream- or buff-coloured mushroom, the
Infundibulicybe_geotropa
Largest living species of fish
longevity of whale sharks, either by analyzing evidence from vertebral growth rings or measurements taken from re-sighted sharks over several years. This information
Whale_shark
Species of tree native to North America
December 5, 2019. "OldList, A Database Of Old Trees". Rocky Mountain Tree-Ring Research. May 2019. Archived from the original on April 12, 2013. Retrieved
Sequoiadendron_giganteum
Species of eagle
1000, the rest mostly died or disappeared) the average distance between ringing and recovery was 44 km (27 mi), averaging 63 km (39 mi) in juveniles and
Golden_eagle
Extinct species of mammoth
The age of a mammoth can be roughly determined by counting the growth rings of its tusks when viewed in cross-section, but this does not account for
Woolly_mammoth
Genus of Late Cretaceous theropod
used the Latin word rex, meaning "king", for the specific name. The full binomial translates to "tyrant lizard the king" or "King Tyrant Lizard", emphasizing
Tyrannosaurus
Ring subset with only nilpotent elements
and by the binomial theorem, (a+b)m+n = 0. Therefore, the set of all nilpotent elements forms an ideal known as the nil radical of a ring. Because the
Nil_ideal
Species of fungus
thin, transient ring. It is similar in appearance to a less common relative Stropharia aeruginosa, but that species has a more robust ring on its stipe,
Stropharia_caerulea
Species of bird
The ring-tailed pigeon (Patagioenas caribaea) is a species of bird in the family Columbidae. It is endemic to Jamaica. The ring-tailed pigeon is monotypic
Ring-tailed_pigeon
Species of penguin
a long lifespan. The average for the species is 6.5 years, but flipper ringing experiments show that in very exceptional cases they may live up to 25
Little_penguin
Species of tree
sculptures and other amenities in and around the building. The tree's rings were counted, revealing its age to be 75, and museum officials hoped it
Ailanthus_altissima
Species of cat native to Africa and Asia
golden with dark spots grouped in rosettes. Its underbelly is white and its ringed tail is shorter than its body. Its pupils are round. Leopards living in
Leopard
Species of fungus
Giacomo Bresadola in 1882. It has white gills and spores. They typically have rings on the stems, Like several other species of the genus Lepiota, it contains
Lepiota_helveola
German polymath and scholar (1777–1855)
sums, in which he solved the main problem by introducing q-analogs of binomial coefficients and manipulating them by several original identities that
Carl_Friedrich_Gauss
Flowering plant in the family Anacardiaceae
chemically-versatile construct, which contains three functional groups: The aromatic ring, the hydroxyl group, and the double bonds in the flanking alkyl chain. These
Cashew
Branch of mathematics
distinguishes between different types of algebraic structures, such as groups, rings, and fields, based on the number of operations they use and the laws they
Algebra
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BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
BINOMIAL RING
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