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On L-O-supplemented modules
Sobre módulos L-O-suplementados
DOI:
https://doi.org/10.15446/recolma.v54n2.93842Palabras clave:
Supplemented module, I-⊕-supplemented module, dual Rickart module, endomorphism ring, V-ring (en)Módulo suplementado, módulo I-⊕-suplementado, módulo Rickart dual, endomorfismo de anillos, V-anillo (es)
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En esta nota nosotros introducimos los módulos L-⊕-suplementados, una generalizacion de los módulos ⊕-suplementados. Un módulo M se dice I-⊕-suplementado si para cada φ ∈ EndR (M), existe un sumando directo L de M tal que Imφ + L = M y Imφ ∩ L « L. Se demuestra que si M es un módulo I-⊕-suplementado con la condición D3 , entonces cada sumando directo de M es I-⊕-suplementado. Demostramos que si M = M1 ⊕ M2 es I-⊕-suplementado tal que M1 y M2 son proyectivos relativos, entonces M1 y M2 son I-⊕-suplementados. Estudiamos algunos anillos cuyos modulos son I-⊕-suplementados.
In this note we introduce L-⊕-supplemented modules as a proper generalization of ⊕-supplemented modules. A module M is called I-⊕-supplemented if for every φ ∈ EndR (M), there exists a direct summand L of M such that Imφ + L = M and Imφ ∩ L « L. It is shown that if M is a I-⊕-supplemented module with D3 condition, then every direct summand of M is I-⊕-supplemented. We prove that if M = M1 ⊕ M2 is I-⊕-supplemented such that M1 and M2 are relative projective, then M1 and M2 are I-⊕-supplemented. We study some rings whose modules are I-⊕-supplemented.
Referencias
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