有限加性范畴中的Krull-Remak-Schmidt分解

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2023-03-01 DOI:10.1016/j.exmath.2022.12.003

Amit Shah

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引用次数: 4

摘要

其中每个对象都有一个Krull-Remak-Schmidt分解的加性范畴，即由具有局部自同态环的对象组成的有限直接和分解，称为Krull-Schmidt范畴。一个荷有限范畴是一个加性范畴A，它存在一个可交换的单位环k，使得A中的每个荷有限集是一个有限长度的k模。本文的目的是证明一个有限范畴是Krull-Schmidt，当且仅当它有分裂幂等，当且仅当每个不可分解对象有一个局部自同态环。

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Krull-Remak-Schmidt decompositions in Hom-finite additive categories

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.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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