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Quasi-projective and quasi-injective modules

Profile image of Anne KoehlerAnne Koehler

1971, Pacific Journal of Mathematics

https://doi.org/10.2140/PJM.1971.36.713
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11 pages

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Abstract

This paper contains results which are needed to prove a decomposition theorem for quasi-projective modules over left perfect rings. An iϋ-module M is called quasi-projective if and only if for every jβ-module A, every jβ-epimorphism q:M-~+ A, and every iϋ-homomorphism f:M->A, there is an f eΈτιά R {M) such that the diagram M M-^A >0 commutes, that is, qof = /. An i?-module M is called quasi-injective if and only if for every iϋ-module A, every jB-monomorphism j: A->M, and jβ-homomorphism /: A-+M, there is an /' e Έnd R (M) such that the diagram 0 >A- !-*M

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