- non-Noetherian ring
- Математика: ненетерово кольцо
Универсальный англо-русский словарь. Академик.ру. 2011.
non-Noetherian ring
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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
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
Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… … Wikipedia
Glossary 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… … Wikipedia
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
Local ring — In abstract algebra, more particularly in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called local behaviour , in the sense of functions defined on varieties or manifolds, or of… … Wikipedia
Cohen–Macaulay ring — In mathematics, a Cohen–Macaulay ring is a particular type of commutative ring, possessing some of the algebraic geometric properties of a nonsingular variety, such as local equidimensionality. They are named for Francis Sowerby Macaulay, who… … Wikipedia
Polynomial ring — In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the … Wikipedia
Nilradical of a ring — For more radicals, see radical of a ring. In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements of the ring. In the non commutative ring case, more care is needed resulting in several related radicals … Wikipedia
Jaffard ring — In mathematics, a Jaffard ring is a type of ring, more general than a Noetherian ring. Formally, a Jaffard ring is a ring R such that:dim R [T] = 1 + dim R, ,where dim denotes Krull dimension. A Jaffard ring that is also an integral domain is… … 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
