Department of Mathematics, University of Mazandaran, Babolsar, Iran
Abstract
Let M be a right R-module. We call M Rad-H-supplemented if for each Y M there exists a direct summand D of M such that (Y + D)/D (Rad(M) + D)/D and (Y + D)/Y (Rad(M) + Y )/Y . It is shown that: (1) Let M = M1M2, where M1 is a fully invariant submodule of M. If M is Rad-H-supplemented, thenM1 andM2 are Rad-H-supplemented. (2) Let M = M1 M2 be a duo module and Rad--supplemented. If M1 is radical M2-sejective (or M2 is radical M1-sejective), then M is Rad-H-supplemented. (3) Let M = n i=1Mi be a finite direct sum of modules. If Mi is generalized radical Mj-projective for all j > i and each Mi is Rad-H-supplemented, then M is Rad-H-supplemented.
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