An alternative perspective on pure-projectivity of modules

Alagoz Y., DURĞUN Y.

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, vol.14, no.2, pp.631-650, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1007/s40863-020-00191-3
  • Journal Name: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.631-650
  • Keywords: Pure-projective modules, Pure-subprojectivity domains, psp-poor modules, Pure-semisimple rings, INJECTIVITY, RINGS
  • Çukurova University Affiliated: Yes

Abstract

The study of pure-projectivity is accessed from an alternative point of view. Given modules M and N, M is said to be N-pure-subprojective if for every pure epimorphism g : B -> N and homomorphism f : M -> N, there exists a homomorphism h : M -> B such that gh = f. For a module M, the pure-subprojectivity domain of M is defined to be the collection of all modules N such that M is N-pure-subprojective. We obtain characterizations for various types of rings and modules, including FP-injective and FP-projective modules, von Neumann regular rings and pure-semisimple rings in terms of pure-subprojectivity domains. As pure-subprojectivity domains clearly include all pure-projective modules, a reasonable opposite to pure-projectivity in this context is obtained by considering modules whose pure-subprojectivity domain consists of only pure-projective. We refer to these modules as psp-poor. Properties of pure-subprojectivity domains and of psp-poor modules are studied.