Goldie-Rad-Supplemented Modules


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TALEBI Y., HAMZEKOLAEE A. R. M., TERCAN A.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.22, sa.3, ss.205-218, 2014 (SCI-Expanded) identifier identifier

Özet

In this paper we introduce beta** relation on the lattice of submodules of a module M. We say that submodules X, Y of M are beta** equivalent, X beta**Y, if and only if X+Y/X subset of Rad(M)+X/X and X+Y/Y subset of Rad(M)+Y/Y We show that the beta** relation is an equivalence relation. We also investigate some general properties of this relation. This relation is used to define and study classes of Goldie-Rad-supplemented and Rad-H-supplemented modules. We prove M = A circle plus B is Goldie-Rad-supplemented if and only if A and B are Goldie-Rad-supplemented.