MODULES THAT HAVE A GENERALIZED delta-SUPPLEMENT IN EVERY COFINITE EXTENSION

Sozen E. O., Eren Ş.

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, vol.40, no.3, pp.241-254, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.17654/nt040030241
  • Journal Name: JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.241-254
  • Keywords: delta-supplement, delta-semiperfect, cofinite extension, SEMIPERFECT, RINGS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we define modules with the properties (delta-GSCE) and (delta-GSCEE) by adapting Zoschinger's modules with the properties (E) and (EE) and we investigate the structure of modules with these properties. It is shown that: (1) a module has the property (delta-GSCEE) iff every submodule has the property (delta-GSCE); (2) the property (delta-GSCE) is inherited by direct summands; (3) for an R-module over a delta-V-ring, M has the property (delta-GSCE) iff M is cofinitely injective; (4) if R is a delta-semiperfect ring, then every left R-module has the property (delta-GSCE).