A uniqueness theorem in a finitely accessible additive category

BERKTAŞ M. K.

Algebras and Representation Theory, cilt.17, sa.3, ss.1009-1012, 2014 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 3
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10468-013-9435-x
  • Dergi Adı: Algebras and Representation Theory
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1009-1012
  • Anahtar Kelimeler: Accessible categories, Cotorsion envelope, Krull Remak Schmidt Theorem, Pure injective envelope
  • Uşak Üniversitesi Adresli: Evet

Özet

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.