On cofinitely weak supplemented modules

Abstract

For a locally noetherian module, we prove some conditions equivalent to being cofinitely weak supplemented. Every semilocal module is cofinitely weak supplemented. For a module M with small radical, it is shown that M is weakly supplemented if and only if every cyclic submodule has a weak supplement. A commutative domain R is h-semilocal if and only if every torsion R-module is cofinitely weak supplemented.