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http://dx.doi.org/10.4134/BKMS.2008.45.1.059

X-LIFTING MODULES OVER RIGHT PERFECT RINGS  

Chang, Chae-Hoon (INFORMATION THCHNOLOGY MANPOWER DEVELOPMENT PROGRAM KYUNGPOOK NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 59-66 More about this Journal
Abstract
Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. 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 $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.
Keywords
right perfect ring; lifting module; exchange property;
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