MMN-397
Characterizations of Rad-supplemented modules
Abstract
We prove that a ring R is Rad-supplemented if and only if every cyclic R-
module has ample Rad-supplements in every f.g. extension of itself. Moreover, we study
on Rad-supplemented modules over commutative noetherian rings. We show that; a
module M is Rad-supplemented if and only if it is an extension of a Rad-supplemented
submodule by a reduced supplemented module; a ring R is semilocal if and only if every
left R-module with Rad-supplemented radical is Rad-supplemented. In addition, we also
prove that every Rad-supplemented module containing a maximal submodule is amply
Rad-supplemented. Finally, we determine the structure of torsion-free Rad-supplemented
modules over non-local dedekind domains.
Vol. 13 (2012), No. 2, pp. 569-580