Rings with modules having a restricted injectivity domain
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019 (ESCI)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası:
- Basım Tarihi: 2019
- Doi Numarası: 10.1007/s40863-019-00153-4
- Dergi Adı: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Anahtar Kelimeler: Injective module, Poor module, Working-class module, Good ring, WV-ring, POOR MODULES, OPPOSITE
- Abdullah Gül Üniversitesi Adresli: Evet
Özet
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.