On Rad-H-supplemented Modules

Document Type: Research articles


Department of Mathematics, University of Mazandaran, Babolsar, Iran


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.