On Krull-Schmidt finitely accessible categories

Authors

  • Septimiu Crivei

Keywords:

Krull-Schmidt category, pure-injective object, semiperfect ring, Osofsky theorem

Abstract

Let $\mathcal{C}$ be a finitely accessible additive category with products, and let $(U_i)_{i\in I}$ be a family of representative classes of finitely presented objects in $\mathcal{C}$ such that each object $U_i$ is pure-injective. We show that $\mathcal{C}$ is a Krull-Schmidt category if and only if every pure epimorphic image of the objects $U_i$ is pure-injective.

Published

2011-10-19

Issue

Vol. 84 No. 1 (2011)

Section

Articles
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