Research Information System
COMMUNICATIONS IN ALGEBRA, vol.44, no.4, pp.1496-1513, 2016 (SCI-Expanded)
Let R be an arbitrary ring with identity and M a right R-module with S=End(R)(M). Let F be a fully invariant submodule of M. We call M an F-inverse split module if f(-1)(F) is a direct summand of M for every fS. This work is devoted to investigation of various properties and characterizations of an F-inverse split module M and to show, among others, the following results: (1) the module M is F-inverse split if and only if M=F circle plus K where K is a Rickart module; (2) for every free R-module M, there exists a fully invariant submodule F of M such that M is F-inverse split if and only if for every projective R-module M, there exists a fully invariant submodule F of M such that M is F-inverse split; and (3) Every R-module M is Z(2)(M)-inverse split and Z(2)(M) is projective if and only if R is semisimple.