Investigating modules with partial endomorphisms having μ-small kernels

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In this paper, we introduce and study the concept of generalized monoform modules ($G-M$ modules, for short) which is a proper generalization of that of monoform modules. We present some of their examples, properties and characterizations. It is shown that over a commutative ring $R$, the properties monoform, small monoform, $G-M$, compressible, uniform and weakly co-Hopfian are all equivalent. Moreover, we demonstrate that a ring $R$ is an injective semisimple ring iff any $R$-module is $G-M$. Further, we prove a similar theorem to Hilbert's basis theorem for monoform, small monoform and $G-M$ modules.
Language:
English
Published:
Journal of Mahani Mathematical Research, Volume:14 Issue: 1, Winter and Spring 2025
Pages:
249 to 262
https://www.magiran.com/p2831498  
سامانه نویسندگان
  • Alireza Moniri Hamzekolaee
    Corresponding Author (2)
    Associate Professor Pure Mathematics-Algebra-Ring and Module Theory, University of Mazandaran, Babolsar, Iran
    Moniri Hamzekolaee، Alireza
  • Samira Asgari
    Author (4)
    .Ph.D Pure Mathematics-Algebra, University of Mazandaran, Babolsar, Iran
    Asgari، Samira
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