Abstract

AMOUZEGAR, Tayyebeh. On L-⊕-supplemented modules. Rev.colomb.mat. [online]. 2020, vol.54, n.2, pp.129-139.  Epub Mar 05, 2021. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v54n2.93842.

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.

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