On Rad-H-supplemented Modules

Abstract

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