UC modules with respect to a torsion theory


Ceken S., ALKAN M.

TURKISH JOURNAL OF MATHEMATICS, vol.36, no.3, pp.376-385, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.3906/mat-1009-33
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.376-385
  • Keywords: Hereditary torsion theory, tau-closed submodule, UC module, tau-UC module
  • Akdeniz University Affiliated: Yes

Abstract

In tins paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod- R by using the concept of tau-closed submodule which was studied in [2]. We compare UC and tau-UC modules and examine the relationships between them. We also give some examples of tau-UC and UC modules and submodules which have a unique tau-closure and unique closure.