Projectivity relative to closed (neat) submodol

Durğun Y.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.21, no.06, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 06
  • Publication Date: 2022
  • Doi Number: 10.1142/s0219498822501146
  • 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: Neat submodules, (C-)pure submodules, closed submodules, closed (neat) projective modules, proper class, PURITY
  • Çukurova University Affiliated: Yes

Abstract

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study closed (neat) projective modules. In particular, the structure of a ring over which every finitely generated (cyclic, injective) right R-module is closed (neat) projective is studied. Furthermore, the relationship among the proper classes which are induced by closed submodules, neat submodules, pure submodules and C-pure submodules are investigated.