Investigating modules with partial endomorphisms having μ-small kernels

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Sciences, University of Mohammed First, Oujda, Morocco

2 Department of Mathematics, University of Mazandaran, Babolsar, Iran

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.

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References

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Journal of Mahani Mathematical Research
Volume 14, Issue 1 - Serial Number 31
January 2025
Pages 249-262

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History

  • Receive Date: 01 May 2024
  • Revise Date: 23 July 2024
  • Accept Date: 27 September 2024

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