Rings with modules having a restricted injectivity domain
| Autor: | Ergül Türkmen, Yılmaz Mehmet Demirci, Burcu Nişancı Türkmen |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Ring (mathematics) Mathematics::Commutative Algebra Generalization General Mathematics 010102 general mathematics Zero (complex analysis) 010103 numerical & computational mathematics 01 natural sciences Injective module Injective function Computational Theory and Mathematics Simple (abstract algebra) Domain (ring theory) 0101 mathematics Statistics Probability and Uncertainty Simple module Mathematics |
| Zdroj: | São Paulo Journal of Mathematical Sciences. 14:312-326 |
| ISSN: | 2316-9028 1982-6907 |
| DOI: | 10.1007/s40863-019-00153-4 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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