Some Results on Simple-Direct-Injective Modules

KESKİN TÜTÜNCÜ D., Tribak R.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.63, no.4, pp.521-537, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.5666/kmj.2023.63.4.521
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.521-537
  • Hacettepe University Affiliated: Yes

Abstract

A module M is called a simple-direct-injective module if, whenever A and B are simple submodules of M with A similar to= B and B is a direct summand of M, then A is a direct summand of M. Some new characterizations of these modules are proved. The structure of simple-direct-injective modules over a commutative Dedekind domain is fully determined. Also, some relevant counterexamples are indicated to show that a left simpledirect-injective ring need not be right simple-direct-injective.