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1 integrally closed domain
Математика: целозамкнутая областьУниверсальный англо-русский словарь > integrally closed domain
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2 integrally closed domain
матем.English-Russian scientific dictionary > integrally closed domain
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3 domain
1) владение, имение2) территория, зона3) физ. домен4) область, сфера5) матем. область определения6) область, домен• -
4 mapping
1) картирование, картографирование, составление карт2) отображение || отображающий•- almost open mapping - almost proper mapping - almost separably-valued mapping - completely regular mapping - correlative mapping - countably biquotient mapping - countably multiple mapping - homotopically regular mapping - homotopically stable mapping - homotopy inverse mapping - locally homeomorphic mapping - locally homomorphic mapping - locally infinitesimal stable mapping
См. также в других словарях:
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
Integrally closed — In mathematics, more specifically in abstract algebra, the concept of integrally closed has two meanings, one for groups and one for rings. Commutative rings Main article: Integrally closed domain A commutative ring R contained in a ring S is… … 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
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
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
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
Integrality — In commutative algebra, the notions of an element integral over a ring (also called an algebraic integer over the ring), and of an integral extension of rings, are a generalization of the notions in field theory of an element being algebraic over … Wikipedia
Integral element — In commutative algebra, an element b of a commutative ring B is said to be integral over its subring A if there are such that That is to say, b is a root of a monic polynomial over A.[1] If B consists of elements that are integral over A, then B… … Wikipedia
Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
Nagata ring — In commutative algebra, an integral domain A is called an N 1 ring if its integral closure in its quotient field is a finitely generated A module. It is called a Japanese ring (or an N 2 ring) if for every finite extension L of its quotient field … Wikipedia
