On the structure of modules defined by subinjectivity

Altinay F., Buyukasik E., DURĞUN Y.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.18, no.10, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 10
  • Publication Date: 2019
  • Doi Number: 10.1142/s0219498819501883
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Injective modules, subinjectivity domain, indigent modules, INJECTIVITY, RINGS, OPPOSITE, POOR
  • Çukurova University Affiliated: Yes

Abstract

The aim of this paper is to present new results and generalize some results about indigent modules. The commutative rings whose simple modules are indigent or injective are fully determined. The rings whose cyclic right modules are indigent are shown to be semisimple Artinian. We give a complete characterization of indigent modules over commutative hereditary Noetherian rings. We show that a reduced module is indigent if and only if it is a Whitehead test module for injectivity over commutative hereditary noetherian rings. Furthermore, Dedekind domains are characterized by test modules for injectivity by subinjectivity.