EPI-RETRACTABLE MODULES AND SOMEAPPLICATIONS

Generalizing concents right Bezout and principa lright ideal of a ring R to modules, an R-modnle M is called n-eptrctrartoble(resp. epi-retTnrtable) if every n-generated submodule(resp. submodule of MR is a homomorphic image of M, It is shown that if MR is finitely generated quasi-projective l-epi-retract.able,then EndR(M) is a right Bezout (resp. principal right ideal) ringif and only if ,MR is n-epi-retractable for all n 1 (resp. cpiretractable).For a ring R and an infinite ordinal β R, the Rmodule M = F +N is epi-retractable where F is a free R-module with a basis sct of cardinality β and IV is a freeR-module.with λ «β .A ring R is quasi Frobenius if every injective R-moduleis epi-retractable. Injective modules in cr[NR ] arc opi-retract.ablefor every N E σ[NR] if and only if every non. zero factor ring of S is a quasi Frobcnins ring where S is an endomorphism ring of aprogenerator in σ[MR]