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Krull–Schmidt category : ウィキペディア英語版 | Krull–Schmidt category In category theory, a Krull–Schmidt category is a generalization of categories in which the Krull–Schmidt theorem holds. They arise, for example, in the study of finite-dimensional modules over an algebra. == Definition ==
Let ''C'' be an additive category, or more generally an additive for a commutative ring . We call ''C'' a Krull-Schmidt category provided that every object decomposes into a finite direct sum of objects having local endomorphism rings. Equivalently, ''C'' has split idempotents and the endomorphism ring of every object is semiperfect.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Krull–Schmidt category」の詳細全文を読む
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