RELATIVE HOMOLOGICAL ALGEBRA IN CATEGORIES OF REPRESENTATIONS OF INFINITE QUIVERS

Estrada S., ÖZDEMİR S.

HOUSTON JOURNAL OF MATHEMATICS, cilt.39, sa.2, ss.343-362, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 2
  • Basım Tarihi: 2013
  • Dergi Adı: HOUSTON JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.343-362
  • Anahtar Kelimeler: Cover, envelope, torsion free, flat, representations of a quiver, QUASI-COHERENT SHEAVES, FLAT COVERS, MODULES
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In the first part of this paper, we prove the existence of torsion free covers in the category of representations of quivers, (Q; R-Mod), for a wide class of quivers included in the class of the so-called source injective representation quivers provided that any direct sum of torsion free and injective R-modules is injective. In the second part, we prove the existence of F-cw-covers and F-cw(perpendicular to)-envelopes for any quiver Q and any ring R with unity, where F-cw is the class of all "componentwise" flat representations of Q.