Generalizations of ⊕ -supplemented modules - Türkmen, B.N.; Pancar, A. (Український математичний журнал, 2013)
We introduce ⊕-radical supplemented modules and strongly ⊕-radical supplemented modules (briefly, srs⊕-modules) as proper generalizations of ⊕-supplemented modules. We prove that (1) a semilocal ring R is left perfect if and only if every left R-module is an ⊕-radical supplemented module; (2) a commutative ring R is an Artinian principal ideal ring if and only if every left R-module is a srs⊕-module; (3) over a local Dedekind domain, every ⊕-radical supplemented module is a srs⊕-module. Moreover, we completely determine the structure of these modules over local Dedekind domains.