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单词 Artinian
释义

artinian


A module M is artinianPlanetmathPlanetmathif it satisfies the following equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath conditions:

  • the descending chain conditionMathworldPlanetmathPlanetmathPlanetmath holds for submodulesMathworldPlanetmath of M;

  • every nonempty family of submodules of M has a minimal element.

A ring R is left artinianif it is artinian as a left module over itself(i.e. if RR is an artinian module),and right artinianif it is artinian as a right module over itself(i.e. if RR is an artinian module),and simply artinian if both conditions hold.

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更新时间:2025/5/5 6:31:26