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X-LIFTING MODULES OVER RIGHT PERFECT RINGS
( Jong Moom Shin ),( Chae Hoon Chang ) 한국수학교육학회 2014 純粹 및 應用數學 Vol.21 No.2
Keskin and Harmanci defined the family β(M,X) = {A ≤ MI ∃Y ≤ X, ∃f ∈ HomR(M,X/Y), Ker f/A ≪ M/A}. And Orhan and Keskin generalized projective modules via the class β(M,X). In this note we introduce X-local summands and X-hollow modules via the class β(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 contains its radical, 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 ∈ β(M,X), if H ㅁ H has the internal exchange property, then H has a local endomorphism ring.