- Krull domain
- Математика: кольцо Крулла
Универсальный англо-русский словарь. Академик.ру. 2011.
Krull domain
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Krull dimension — In commutative algebra, the Krull dimension of a ring R, named after Wolfgang Krull (1899–1971), is the supremum of the number of strict inclusions in a chain of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. A… … Wikipedia
Krull ring — A Krull ring is a particular type of commutative ring studied in commutative algebra and related branches of mathematics and named after the German mathematician Wolfgang Krull.Formal definitionLet A be an integral domain and let P be the set of… … 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
Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… … Wikipedia
КЛАССОВ ДИВИЗОРОВ ГРУППА — факторгруппа группы диеизориалъных идеалов D (А) Крулля кольца А по подгруппе главных идеалов F(A). К. д. г. является абелевой группой и обычно обозначается С(А). Группа С(А)порождается классами простых идеалов высоты 1 в кольце А. В некотором… … Математическая энциклопедия
Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with … 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
Serial module — Chain ring redirects here. For the bicycle part, see Chainring. In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M,… … Wikipedia
Discrete valuation ring — In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non zero maximal ideal. This means a DVR is an integral domain R which satisfies any one of the following equivalent conditions: R is a local… … Wikipedia
Noetherian ring — In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non empty set of ideals has a maximal element. Equivalently, a ring is Noetherian if it… … Wikipedia
