- chain of ideals
- мат.цепь идеалов
English-Russian scientific dictionary. 2008.
chain of ideals
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Chain complete — In mathematics, a partially ordered set in order theory is chain complete if every chain in it has a least upper bound. Unlike complete posets, chain complete posets are relatively common. Examples include: Any complete poset The set of all… … Wikipedia
Ascending chain condition on principal ideals — In abstract algebra, the ascending chain condition can be applied to the posets of principal left, principal right, or principal two sided ideals of a ring, partially ordered by inclusion. The ascending ascending chain condition on principal… … Wikipedia
Ascending chain condition — The ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly, ideals in certain commutative rings.[1][2][3] These conditions played an important role… … 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
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
Noetherian topological space — In mathematics, a Noetherian topological space is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the… … Wikipedia
noetherian — adjective a) Of a ring in which any ascending chain of ideals eventually starts repeating. b) Of a module in which any ascending chain of submodules eventually starts repeating … Wiktionary
Artinian — adjective a) (Of a ring) in which any descending chain of ideals eventually starts repeating. b) (Of a module) in which any descending chain of submodules eventually starts repeating … Wiktionary
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
Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) … Wikipedia
Going up and going down — In commutative algebra, a branch of mathematics, going up and going down are terms which refer to certain properties of chains of prime ideals in integral extensions. The phrase going up refers to the case when a chain can be extended by upward… … Wikipedia
