@article { author = {Hosseinpour, M. and Moniri Hamzekolaee, A. R.}, title = {A KIND OF F-INVERSE SPLIT MODULES}, journal = {Journal of Algebraic Systems}, volume = {7}, number = {2}, pages = {167-178}, year = {2020}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2019.7211.1353}, abstract = {Let M be a right module over a ring R. In this manuscript, we shall study on a special case of F-inverse split modules where F is a fully invariant submodule of M introduced in [12]. We say M is Z 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct summand of M for each endomorphism f of M. We prove that M is Z2(M)-inverse split if and only if M is a direct sum of Z2(M) and a Z2-torsionfree Rickart submodule. It is shown under some assumptions that the class of right perfect rings R for which every right R-module M is Z2(M)-inverse split (Z(M)-inverse split) is precisely that of right GV-rings.}, keywords = {Rickart module,Z(M)-inverse split module,Z^2(M)-inverse split module}, url = {https://jas.shahroodut.ac.ir/article_1587.html}, eprint = {https://jas.shahroodut.ac.ir/article_1587_488e6eda3752698fdd43a0b3c52a0dde.pdf} }