A KIND OF F-INVERSE SPLIT MODULES

Abstract

Let M be a right module over a ring R. In this manuscript,<br /> we shall study on a special case of F-inverse split modules<br /> where F is a fully invariant submodule of M introduced in [12].<br /> We say M is Z<br /> 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct<br /> summand of M for each endomorphism f of M. We prove that M<br /> is Z2(M)-inverse split if and only if M is a direct sum of Z2(M)<br /> and a Z2-torsionfree Rickart submodule. It is shown under some<br /> assumptions that the class of right perfect rings R for which every<br /> right R-module M is Z2(M)-inverse split (Z(M)-inverse split) is<br /> precisely that of right GV-rings.