Shahrood University of TechnologyJournal of Algebraic Systems2345-51287220200101A KIND OF F-INVERSE SPLIT MODULES167178158710.22044/jas.2019.7211.1353ENM.HosseinpourDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.A. R.Moniri HamzekolaeeDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.0000-0002-2852-7870Journal Article20180630Let 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.http://jas.shahroodut.ac.ir/article_1587_488e6eda3752698fdd43a0b3c52a0dde.pdf