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单词 SemilocalRing
释义

semi-local ring


A ring R is semi-local if R/rad(R) is an Artinian ring, where rad(R) denotes the Jacobson radicalMathworldPlanetmath of R. In the case that R is commutativePlanetmathPlanetmathPlanetmath, this reduces to the definition that R is semi-local if R has finitely many maximal idealsMathworldPlanetmath. Note that finite rings are trivially semi-local.

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更新时间:2025/5/3 12:33:16