On π - Morphic Modules

Authors : A. HARMANCİ, H. KOSE, Y. KURTULMAZ

Pages : 411-418

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Publication Date : 2013-04-01

Article Type : Other Papers

Abstract :Let R be an arbitrary ring with identity and M be a right R-modulewith S = Endinsert ignore into journalissuearticles values(MR );. Let f∈ S. f is called π-morphic if M/fn insert ignore into journalissuearticles values(M ); ∼= r M insert ignore into journalissuearticles values(f n ); for some positive integer n. A module M is called π-morphicif every f∈ S is π-morphic. It is proved that M is π-morphic andimage-projective if and only if S is right π-morphic and M generates itskernel. S is unit-π-regular if and only if M is π-morphic and π-Rickartif and only if M is π-morphic and dual π-Rickart. M is π-morphic andimage-injective if and only if S is left π-morphic and M cogenerates itscokernel.
Keywords : Endomorphism rings, π morphic rings, π morphic modules, unit π regularrings