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单词 CohenMacaulayModule
释义

Cohen-Macaulay module


A module M over a ring R is a Cohen-Macaulay module if its depth is defined and equals its Krull dimension. A ring is said to be Cohen-Macaulay (or just C-M) if it is a Cohen-Macaulay module viewed as a module over itself.

Cohen-Macaulay rings are used extensively in combinatorial geometry and commutative ring theory, and has applications to algebraic geometryMathworldPlanetmathPlanetmath as well. For instance, a variety all of whose local ringsMathworldPlanetmath are Cohen-Macaulay has, in a sense, nicer behaviour than an arbitrary singular variety.

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更新时间:2025/5/4 13:25:10