Proper Classes Generated by Isosimple Modules

Özdemir S., Türkoğlu Z.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.4134/bkms.b230541
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1-15
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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).