TY - JOUR
ID - 1587
TI - A KIND OF F-INVERSE SPLIT MODULES
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Hosseinpour, M.
AU - Moniri Hamzekolaee, A. R.
AD - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran,
P.O. Box 47416-95447, Babolsar, Iran.
Y1 - 2020
PY - 2020
VL - 7
IS - 2
SP - 167
EP - 178
KW - Rickart module
KW - Z(M)-inverse split module
KW - Z^2(M)-inverse split module
DO - 10.22044/jas.2019.7211.1353
N2 - 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.
UR - http://jas.shahroodut.ac.ir/article_1587.html
L1 - http://jas.shahroodut.ac.ir/article_1587_488e6eda3752698fdd43a0b3c52a0dde.pdf
ER -