On complete pure-injectivity in locally finitely presented categories

BERKTAŞ M. K., Crivei S.

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, vol.59, no.4, pp.331-337, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 4
  • Publication Date: 2016
  • Journal Name: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.331-337
  • Keywords: (completely) pure-injective object, Indecomposable decomposition, Krull-Schmidt category, Locally finitely presented category, Osofsky theorem, Semiperfect ring, Semisimple ring
  • Uşak University Affiliated: Yes

Abstract

Let C be a locally finitely presented additive category, and let E be a finitely presented pure-injective object of C. We prove that E has an indecomposable decomposition if and only if every pure epimorphic image of E is pure-injective if and only if the endomorphism ring of E is semiperfect. This extends a module-theoretic result which generalises the classical Osofsky Theorem.