Minus partial order in regular modules

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ÜNGÖR B., HALICIOĞLU S., Harmanci A., Marovt J.

COMMUNICATIONS IN ALGEBRA, vol.48, no.10, pp.4542-4553, 2020 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 10
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2020.1766056
  • 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.4542-4553
  • Keywords: Minus partial order, regular module, LEFT-STAR
  • Ankara University Affiliated: Yes

Abstract

The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation to the module theoretic setting and prove that this relation is a partial order when the module is regular. Moreover, various characterizations of the minus partial order in regular modules are presented and some well-known results are also generalized.