irreducible element

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• Irreducible (mathematics) — In mathematics, the term irreducible is used in several ways. * In abstract algebra, irreducible can be an abbreviation for irreducible element; for example an irreducible polynomial. * In representation theory, an irreducible representation is a …   Wikipedia

• element — [el′ə mənt] n. [ME < OFr < L elementum, first principle, element] 1. any of the four substances (earth, air, fire, and water) formerly believed to constitute all physical matter 2. any of these four substances thought of as the natural… …   English World dictionary

• element — element, component, constituent, ingredient, factor are comparable when they mean one of the parts, substances, or principles which make up a compound or complex thing. Element is, except in its specific sense in science, the most widely… …   New Dictionary of Synonyms

• Irreducible polynomial — In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non trivial factors in a given set. See also factorization. For any field F , the ring of polynomials with coefficients in F is… …   Wikipedia

• element — I (New American Roget s College Thesaurus) n. component, part, substance, constituent, ingredient; factor, principle, rudiment, fundamental. See cause, composition. II (Roget s IV) n. 1. [A part] Syn. component, constituent, factor, ingredient,… …   English dictionary for students

• element — noun Etymology: Middle English, from Anglo French & Latin; Anglo French, from Latin elementum Date: 13th century 1. a. any of the four substances air, water, fire, and earth formerly believed to compose the physical universe b. plural weather… …   New Collegiate Dictionary

• Subdirect irreducible — In algebra, a subdirect irreducible is an algebra that cannot be factored as a subdirect product of simpler algebras. Subdirect irreducibles play a somewhat analogous role in algebra to primes in number theory. TOC =Definition=In algebra, a… …   Wikipedia

• Coxeter element — Not to be confused with Longest element of a Coxeter group. In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group, hence also of a root system or its Weyl group. It is named after H.S.M.… …   Wikipedia

• Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

• Integral domain — In abstract algebra, an integral domain is a commutative ring that has no zero divisors,[1] and which is not the trivial ring {0}. It is usually assumed that commutative rings and integral domains have a multiplicative identity even though this… …   Wikipedia

• Unique factorization domain — In mathematics, a unique factorization domain (UFD) is, roughly speaking, a commutative ring in which every element, with special exceptions, can be uniquely written as a product of prime elements, analogous to the fundamental theorem of… …   Wikipedia