ON SUBINJECTIVITY DOMAINS OF PURE-INJECTIVE MODULES

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DURĞUN Y.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.51, no.4, pp.1227-1238, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1216/rmj.2021.51.1227
  • Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1227-1238
  • Keywords: pure-injective module, subinjective domain, pi-indigent module, absolutely pure module, ALTERNATIVE PERSPECTIVE, RINGS, PURITY
  • Çukurova University Affiliated: Yes

Abstract

A pure-injective module M is said to be pi-indigent if its subinjectivity domain is smallest possible, namely, consisting of exactly the absolutely pure modules. A module M is called subinjective relative to a module N if for every extension K of N, every homomorphism N -> M can be extended to a homomorphism K -> M. The subinjectivity domain of the module M is defined to be the class of modules N such that M is N-subinjective. Basic properties of the subinjectivity domains of pure-injective modules and of pi-indigent modules are studied. The structure of a ring over which every simple, uniform, or indecomposable pure-injective module is injective or subinjective relative only to the smallest possible family of modules is investigated.