A New Characterization of Commutative Strongly $\Pi$-Regular Rings

  •  Anta Gueye    
  •  Cheikh Gueye    
  •  Mamadou Sanghare    


Let $R$ be a commutative ring. It is known that any injective endomorphism of finitely generated $R$-module is an isomorphism if and only if every prime ideal of $R$ is maximal. This result makes possible a characterization of rings on which all finitely generated modules are co-hopfian. The motivation of this paper comes from trying to extend these results to mono-correct modules. In doing so, we show that any finitely generated $R$-module is mono-correct if and only if every prime ideal of $R$ is maximal and we  obtain a characterization of commutative rings on which all finitely generated module are mono-correct. Such rings are exactly commutative strongly $\Pi$-regular rings. So we have a new characterization of commutative strongly $\Pi$-regular rings.

This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1916-9795
  • ISSN(Online): 1916-9809
  • Started: 2009
  • Frequency: bimonthly

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