The direct sum order in regular modules

ÜNGÖR B., HALICIOĞLU S., Harmanci A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.19, no.9, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 9
  • Publication Date: 2020
  • Doi Number: 10.1142/s0219498820501789
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we define the direct sum relation on a module and prove that this is a partial order when the module is regular. We also focus on a regular support and a strong regular support of an element in a module, which are extensions of a generalized inverse and a reflexive generalized inverse of an element in a ring, respectively. Using regular supports and strong regular supports, we present various characterizations of the direct sum order as an application. We obtain some decompositions of a module via the direct sum order.