- factorization domain
- мат.область разложения (на множители)
English-Russian scientific dictionary. 2008.
factorization domain
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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
Noncommutative unique factorization domain — In mathematics, the noncommutative unique factorization domain is the noncommutative counterpart of the commutative or classical unique factorization domain (UFD). Example The ring of integral quaternions. If the coefficients a0, a1, a2, a3 are… … Wikipedia
Domain — may refer to: General Territory (administrative division), a non sovereign geographic area which has come under the authority of another government Public domain, a body of works and knowledge without proprietary interest Eminent domain, the… … 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
Dedekind domain — In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily … Wikipedia
Integrally closed domain — In commutative algebra, an integrally closed domain A is an integral domain whose integral closure in the field of fractions of A is A itself. Many well studied domains are integrally closed: Fields, the ring of integers Z, unique factorization… … Wikipedia
GCD domain — A GCD domain in mathematics is an integral domain R with the property that any two non zero elements have a greatest common divisor (GCD). Equivalently, any two non zero elements of R have a least common multiple (LCM). [cite book|author=Scott T … Wikipedia
Bézout domain — In mathematics, a Bézout domain is an integral domain which is, in a certain sense, a non Noetherian analogue of a principal ideal domain. More precisely, a Bézout domain is a domain in which every finitely generated ideal is principal. A… … Wikipedia
Principal ideal domain — In abstract algebra, a principal ideal domain, or PID is an integral domain in which every ideal is principal, i.e., can be generated by a single element.Principal ideal domains are thus mathematical objects which behave somewhat like the… … Wikipedia
Euclidean domain — In abstract algebra, a Euclidean domain (also called a Euclidean ring) is a type of ring in which the Euclidean algorithm applies. A Euclidean domain is a specific type of integral domain, and can be characterized by the following (not… … Wikipedia
Integer factorization — In number theory, integer factorization is the way of breaking down a composite number into smaller non trivial divisors, which when multiplied together equal the original integer.When the numbers are very large, no efficient integer… … Wikipedia
