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ON KRULL–SCHMIDT FINITELY ACCESSIBLE CATEGORIES

Part of: Categories and theories

Published online by Cambridge University Press:  01 April 2011

SEPTIMIU CRIVEI
SEPTIMIU CRIVEI*
Affiliation:
Faculty of Mathematics and Computer Science, ‘Babeş-Bolyai’ University, Str. M. Kogălniceanu 1, 400084 Cluj-Napoca, Romania (email: crivei@math.ubbcluj.ro)
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Abstract

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

Keywords

Krull–Schmidt categorypure-injective objectsemiperfect ringOsofsky theorem

MSC classification

Secondary: 18C35: Accessible and locally presentable categories
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 90 - 97
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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