H-SUPPLEMENTED MODULES WITH SMALL RADICAL

Abstract

We say that a module M is H-supplemented if for every submodule A there is a direct summand B such that A + X = M holds if and only if B +X = M. This paper investigates the structure of H-supplemented modules over commutative noetherian rings. After reducing this question to the case of local rings and describing H-supplemented modules with small radical, it is shown that if every direct summand of M is H-supplemented, then M is a direct sum of hollow modules. In the second part of this paper it is studied some rings whose modules are H-supplemented.