Pure-direct-projective modules

ALİZADE R., TOKSOY S. E.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498824500105
  • 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
  • Keywords: (Pure-)direct-projective modules, (pure-)projective modules, von Neumann regular rings, RINGS
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we introduce and study the pure-direct-projective modules, that is the modules M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct. summand of M. We characterize rings over which every right R-module is pure-direct-projective. We examine for which rings or under what conditions pure-direct-projective right R-modules are direct-projective, projective, quasi-projective, pure-projective, flat or injective. We prove that over a Noetherian ring every injective module is pure-direct-projective and a right hereditary ring R is right Noetherian if and only if every injective right R-module is pure-direct-projective. We obtain some properties of pure-direct-projective right R-modules which have DPSP and DPIP.