A uniqueness theorem in a finitely accessible additive category

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BERKTAŞ M. K.

Algebras and Representation Theory, vol.17, no.3, pp.1009-1012, 2014 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 17 Issue: 3
• Publication Date: 2014
• Doi Number: 10.1007/s10468-013-9435-x
• Journal Name: Algebras and Representation Theory
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.1009-1012
• Keywords: Accessible categories, Cotorsion envelope, Krull Remak Schmidt Theorem, Pure injective envelope
• Uşak University Affiliated: Yes

Abstract

It is proved that if A1,A 2,., Am and B1,B2,..., B n are objects in a finitely accessible additive category A such that their pure injective envelopes are indecomposable, and there are pure monomorphisms μ:A 1∈ ⊕∈A 2∈⊕∈.∈⊕∈A m →B 1∈⊕∈B 2∈⊕∈. ∈⊕∈B n and ν:B 1∈⊕∈B 2∈⊕∈.∈⊕∈B n →A 1∈⊕∈A 2∈⊕∈. ∈⊕∈A m, then m∈=∈n and there are a permutation σ and pure monomorphisms A i →B σ(i) and B σ(i)→A i for every i∈=∈1, 2,., n. © 2013 Springer Science+Business Media Dordrecht.