Rings with modules having a restricted injectivity domain

DEMİRCİ Y. M., TÜRKMEN B. N., TÜRKMEN E.

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume:
  • Publication Date: 2019
  • Doi Number: 10.1007/s40863-019-00153-4
  • Journal Name: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Keywords: Injective module, Poor module, Working-class module, Good ring, WV-ring, POOR MODULES, OPPOSITE
  • Abdullah Gül University Affiliated: Yes

Abstract

We introduce modules whose injectivity domains are contained in the class of modules with zero radical and call them working-class. This notion gives a generalization of poor modules that have minimal injectivity domain. Semisimple working-class modules always exist for arbitrary rings whereas their predecessors do not. We investigate the rings over which every module is either injective or working-class. Right weakly V-rings are examples of these rings. Moreover, we study the existence of working-class simple modules and show that if there is a projective working-class simple right module, then the ring is a right GV-ring.