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.
Hosseinpour, M., & Moniri Hamzekolaee, A. R. (2020). A KIND OF F-INVERSE SPLIT MODULES. Journal of Algebraic Systems, 7(2), 167-178. doi: 10.22044/jas.2019.7211.1353
MLA
M. Hosseinpour; A. R. Moniri Hamzekolaee. "A KIND OF F-INVERSE SPLIT MODULES", Journal of Algebraic Systems, 7, 2, 2020, 167-178. doi: 10.22044/jas.2019.7211.1353
HARVARD
Hosseinpour, M., Moniri Hamzekolaee, A. R. (2020). 'A KIND OF F-INVERSE SPLIT MODULES', Journal of Algebraic Systems, 7(2), pp. 167-178. doi: 10.22044/jas.2019.7211.1353
VANCOUVER
Hosseinpour, M., Moniri Hamzekolaee, A. R. A KIND OF F-INVERSE SPLIT MODULES. Journal of Algebraic Systems, 2020; 7(2): 167-178. doi: 10.22044/jas.2019.7211.1353
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