Modules whose partial endomorphisms have a ?-small kernels

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0059

Keywords:

Small submodules, δ-small submodules, Monoform modules, δ-small monoform modules, Artinian principal ideal ring

Abstract

Let R be a commutative ring and M a unital R-module. A submodule N is said to be ?-small, if whenever N + L = M with M/L is singular, we have L = M. M is called ?-small monoform if any of its partial endomorphism has ?-small kernel. In this paper, we introduce the concept of ?-small monoform modules as a generalization of monoform modules and give some of their properties, examples and characterizations.

Author Biographies

Papa Cheikhou Diop, Université de Thiès.

Dépt. de Mathématiques.

Abdoul Djibril Diallo , Université Cheikh Anta Diop.

Dépt. de Mathématiques et Informatique.

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Published

2020-07-28

How to Cite

[1]
P. C. Diop and A. D. Diallo, “Modules whose partial endomorphisms have a ?-small kernels”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 945-962, Jul. 2020.