On &#960 - Morphic Modules

Abstract

Let R be an arbitrary ring with identity and M be a right R-modulewith S = End(MR ). Let f∈ S. f is called π-morphic if M/fn (M ) ∼= r M (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.

On &#960 - Morphic Modules

Abstract

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Keywords

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References

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