Generalizations of -supplemented modules - Pancar, A.; Türkmen, B. N. (Ukrains’kyi Matematychnyi Zhurnal, 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.