The torsion theory cogenerated by delta-M-small modules and gco-modules

Ozcan A. Ç.

COMMUNICATIONS IN ALGEBRA, vol.35, no.2, pp.623-633, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1080/00927870601074871
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.623-633
  • Hacettepe University Affiliated: Yes

Abstract

Let M be a module and K a suhmodule of a module N in sigma[M]. We call K a delta-M-small submodule of N if whenever N = K + L, NIL is M-singular for any suhmodule L of N, we have N = L. Also we call N a delta-M-small module if N is a delta-M-small submodule of its M-injective hull. In this article, we consider (Z) over bar (delta M)(N) = Rej(N, DM), the reject of DM in N, where DM is the class of all delta-M-small modules. We investigate the properties of (Z) over bar (delta M) (N) and consider the torsion theory tau(delta V) in sigma[M] cogenerated by DM. We compare the tau(delta V) and the torsion theory tau(V) cogenerated by M-small modules and finally we give a characterization of GCO-modules.