TY - JOUR
ID - 451
TI - Applications of Epi-Retractable and Co-Epi-Retractable Modules
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Mostafanasab, H.
AD - Isfahan university of Technology
Y1 - 2013
PY - 2013
VL - 39
IS - 5
SP - 903
EP - 917
KW - MSC(2010): Primary: 16D10, 16S50
KW - Secondary: 16D40, 16E60
DO -
N2 - A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable R-module. A co-pli strongly prime ring R is a simple ring. A left self-injective co-pli ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a pli ring if and only if it is a co-pri ring. Moreover, if R is a left perfect ring such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius ring.
UR - http://bims.iranjournals.ir/article_451.html
L1 - http://bims.iranjournals.ir/article_451_a85b04c9d7350c032000bab9ef5951af.pdf
ER -