On complete pure-injectivity in locally finitely presented categories

BERKTAŞ M. K., Crivei S.

Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, cilt.59, sa.4, ss.331-337, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 4
  • Basım Tarihi: 2016
  • Dergi Adı: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.331-337
  • Anahtar Kelimeler: (completely) pure-injective object, Indecomposable decomposition, Krull-Schmidt category, Locally finitely presented category, Osofsky theorem, Semiperfect ring, Semisimple ring
  • Uşak Üniversitesi Adresli: Evet

Özet

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.