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.
Mostafanasab, H. (2013). Applications of Epi-Retractable and Co-Epi-Retractable Modules. Bulletin of the Iranian Mathematical Society, 39(5), 903-917.
MLA
H. Mostafanasab. "Applications of Epi-Retractable and Co-Epi-Retractable Modules". Bulletin of the Iranian Mathematical Society, 39, 5, 2013, 903-917.
HARVARD
Mostafanasab, H. (2013). 'Applications of Epi-Retractable and Co-Epi-Retractable Modules', Bulletin of the Iranian Mathematical Society, 39(5), pp. 903-917.
VANCOUVER
Mostafanasab, H. Applications of Epi-Retractable and Co-Epi-Retractable Modules. Bulletin of the Iranian Mathematical Society, 2013; 39(5): 903-917.
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