On rings with one middle class of injectivity domains

Alizade R., DEMİRCİ Y. M., Türkmen B. N., Türkmen E.

Mathematical Communications, vol.27, no.1, pp.109-126, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 1
  • Publication Date: 2022
  • Journal Name: Mathematical Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.109-126
  • Keywords: injective module, poor module, modest module, SSI-ring, V-ring, WV-ring, Noetherian ring, POOR MODULES
  • Kayseri University Affiliated: No

Abstract

© 2022 Department of Mathematics, University of Osijek.A module M is said to be modest if the injectivity domain of M is the class of all crumbling modules. In this paper, we investigate the basic properties of modest modules. We provide characterizations of some classes of rings using modest modules. In particular, we show that a ring having the class of crumbling modules as the only right middle class of injectivity domains is either a right V-ring or right Noetherian; and a commutative ring with this property is regular. We also give criteria for a ring having the class of crumbling modules as the only right middle class of injectivity domains.