Proper Classes Generated by Isosimple Modules

Özdemir S., Türkoğlu Z.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.1, pp.1-15, 2024 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 1
  • Publication Date: 2024
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.1-15
  • Dokuz Eylül University Affiliated: Yes

Abstract

The proper class projectively generated by isosimple modules and that injectively generated by isosimple modules do not coincide in general, even for abelian groups. We characterize the commutative principal ideal domains in which these two proper classes coincide. We determine some closure properties of the coprojectives of the latter proper class, and characterize the rings whose all modules are such coprojectives: right strongly V-rings (i.e. rings whose all isosimple modules are injective).