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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.54 no.2 Bogotá jul./dez. 2020 Epub 05-Mar-2021
https://doi.org/10.15446/recolma.v54n2.93842
Artículos originales
On L-⊕-supplemented modules
Sobre módulos L-⊕-suplementados
1 Quchan University of Technology, Quchan, Iran
In this note we introduce L-⊕-supplemented modules as a proper generalization of ⊕-supplemented modules. A module M is called L-⊕-supplemented if for every ø ∈ End R øM), there exists a direct summand L of M such that Imø + L = M and Imø « L. It is shown that if M is a L-⊕-supplemented module with D 3 condition, then every direct summand of M is L ⊕-supplemented. We prove that if M = M 1 ⊕ M 2 is L-⊕-supplemented such that M 1 and M 2 are relative projective, then M 1 and M 2 are L-⊕-supplemented. We study some rings whose modules are L-⊕-supplemented.
Keywords: Supplemented module; L-⊕-supplemented module; dual Rickart module; endomorphism ring; V-ring
En esta nota nosotros introducimos los módulos L-⊕-suplementados, una generalización de los módulos ⊕-suplementados. Un módulo M se dice L-⊕-suplementado si para cada ø ∈ End R øM), existe un sumando directo L de M tal que Imø + L = M y Imø « L. Se demuestra que si M es un módulo L-⊕-suplementado con la condición D 3, entonces cada sumando directo de M es L-⊕-suplementado. Demostramos que si M = M 1 ⊕ M 2 es L-⊕-suplementado tal que M 1 y M 2 son proyectivos relativos, entonces M 1 y M 2 son L-⊕-suplementados. Estudiamos algunos anillos cuyos módulos son L⊕-suplementados.
Palabras clave: Módulo suplementado; módulo I-⊕-suplementado; módulo Rickart dual; endomorfismo de anillos; V -anillo
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Received: January 06, 2020; Accepted: August 13, 2020