Goldie extending property on the class of exact submodules

TERCAN A., YAŞAR R., CELEP YÜCEL C.

COMMUNICATIONS IN ALGEBRA, vol.50, no.4, pp.1363-1371, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1080/00927872.2021.1980580
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1363-1371
  • Keywords: ES-module, exact submodule, Goldie-extending module, left exact preradical, rational hull
  • Hacettepe University Affiliated: Yes

Abstract

We define a module M to be G'-extending if for each exact 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 G'-extending modules and locate the implications between the other extending properties. We study decomposition theory and extensions for G'-extending concept. We show that if a ring is right G'-extending, then so its essential overring. It is shown that G'-extending property is inherited by its rational hull. We provide examples by making special choices of left exact preradicals.