X-LIFTING MODULES OVER RIGHT PERFECT RINGS

Title & Authors
X-LIFTING MODULES OVER RIGHT PERFECT RINGS
Chang, Chae-Hoon;

Abstract
Keskin and Harmanci defined the family B(M,X) = $\small{{A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $\small{K{\in}B}$(H, X), if $\small{H{\oplus}H}$ has the internal exchange property, then H has a local endomorphism ring.
Keywords
right perfect ring;lifting module;exchange property;
Language
English
Cited by
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ON THE DECOMPOSITION OF EXTENDING LIFTING MODULES,;;

대한수학회보, 2009. vol.46. 6, pp.1069-1077
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Characterizations of Several Modules Relative to the Class of B(M, X),;;

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1.
Rings Whose Nonsingular Modules Have Projective Covers, Ukrainian Mathematical Journal, 2016, 68, 1, 1
2.
ON THE DECOMPOSITION OF EXTENDING LIFTING MODULES, Bulletin of the Korean Mathematical Society, 2009, 46, 6, 1069
3.
Characterizations of Several Modules Relative to the Class of B(M, X), Kyungpook mathematical journal, 2013, 53, 1, 37
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