krull ring
1Krull 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… …
2Krull 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… …
3Krull's theorem — In mathematics, more specifically in ring theory, Krull s theorem, named after Wolfgang Krull, proves the existence of maximal ideals in any unital commutative ring. The theorem was first stated in 1929 and is equivalent to the axiom of choice.… …
4Ring (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… …
5Krull's principal ideal theorem — In commutative algebra, Krull s principal ideal theorem, named after Wolfgang Krull (1899 1971), gives a bound on the height of a principal ideal in a Noetherian ring. The theorem is sometimes referred to by its German name, Krulls Hauptidealsatz …
6Wolfgang Krull — Pour les articles homonymes, voir Krull. Wolfgang Krull, Göttingen 1920 Wolfgang Krull (26 août 1899 …
7Wolfgang Krull — (26 August 1899 12 April 1971) was a German mathematician, working in the field of commutative algebra. He was born in Baden Baden, Germany and died in Bonn, Germany. See also * Krull dimension * Krull topology * Krull s intersection theorem *… …
8Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… …
9Regular local ring — In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is exactly the same as its Krull dimension. The minimal number of generators of the maximal… …
10Commutative 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 …
