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- W4313856887 abstract "An additive category in which each object has a Krull-Remak-Schmidt decomposition—that is, a finite direct sum decomposition consisting of objects with local endomorphism rings—is known as a Krull-Schmidt category. A Hom-finite category is an additive category A for which there is a commutative unital ring k, such that each Hom-set in A is a finite length k-module. The aim of this note is to provide a proof that a Hom-finite category is Krull-Schmidt, if and only if it has split idempotents, if and only if each indecomposable object has a local endomorphism ring." @default.
- W4313856887 created "2023-01-10" @default.
- W4313856887 creator A5090226373 @default.
- W4313856887 date "2023-03-01" @default.
- W4313856887 modified "2023-10-16" @default.
- W4313856887 title "Krull-Remak-Schmidt decompositions in Hom-finite additive categories" @default.
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- W4313856887 doi "https://doi.org/10.1016/j.exmath.2022.12.003" @default.
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