GOLDIE EXTENDING PROPERTY ON THE CLASS OF z-CLOSED SUBMODULES

TERCAN A., YAŞAR R., CELEP YÜCEL C.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.59, no.2, pp.453-468, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.4134/bkms.b210349
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.453-468
  • Keywords: Complement, extending module, z-closed, CLS-module, Goldie extending module, rational Hull, MODULES, HULLS, RING
  • Hacettepe University Affiliated: Yes

Abstract

In this article, we define a module M to be G(z)-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X boolean AND D is essential in both X and D. We investigate structural properties of G(z)-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for G(z-)extending modules. We obtain that if a ring is right G(z)-extending, then so is its essential overring. Also it is shown that the G(z)-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right G(z)-extending ring.