RELATIVE HOMOLOGICAL ALGEBRA IN CATEGORIES OF REPRESENTATIONS OF INFINITE QUIVERS


Estrada S., ÖZDEMİR S.

HOUSTON JOURNAL OF MATHEMATICS, vol.39, no.2, pp.343-362, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 2
  • Publication Date: 2013
  • Journal Name: HOUSTON JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.343-362
  • Keywords: Cover, envelope, torsion free, flat, representations of a quiver, QUASI-COHERENT SHEAVES, FLAT COVERS, MODULES
  • Dokuz Eylül University Affiliated: Yes

Abstract

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.