PURE-INJECTIVITY FROM A DIFFERENT PERSPECTIVE

Lopez-Permouth S. R., Mastromatteo J., Tolooei Y., ÜNGÖR B.

GLASGOW MATHEMATICAL JOURNAL, vol.60, no.1, pp.135-151, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1017/s0017089516000616
  • Journal Name: GLASGOW MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.135-151
  • Ankara University Affiliated: Yes

Abstract

The study of pure-injectivity is accessed from an alternative point of view. A module M is called pure-subinjective relative to a module N if for every pure extension K of N, every homomorphism N -> M can be extended to a homomorphism K -> M. The pure-subinjectivity domain of the module M is defined to be the class of modules N such that M is N-pure-subinjective. Basic properties of the notion of pure-subinjectivity are investigated. We obtain characterizations for various types of rings and modules, including absolutely pure (or, FP-injective) modules, von Neumann regular rings and (pure-) semisimple rings in terms of pure-subinjectivity domains. We also consider cotorsion modules, endomorphism rings of certain modules, and, for a module N, (pure) quotients of N-pure-subinjective modules.