Geodesic
Weakly Projective and Weakly Injective Modules
Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 971-981

Voir la notice de l'article provenant de la source Cambridge University Press

A module M is said to be weakly N-projective if it has a projective cover π: P(M) ↠M and for each homomorphism : P(M) → N there exists an epimorphism σ:P(M) ↠M such that (kerσ) = 0, equivalently there exists a homomorphism :M ↠N such that σ= . A module M is said to be weakly projective if it is weakly N-projective for all finitely generated modules N. Weakly N-injective and weakly injective modules are defined dually. In this paper we study rings over which every weakly injective right R-module is weakly projective. We also study those rings over which every weakly projective right module is weakly injective. Among other results, we show that for a ring R the following conditions are equivalent:(1) R is a left perfect and every weakly projective right R-module is weakly injective.(2) R is a direct sum of matrix rings over local QF-rings.(3) R is a QF-ring such that for any indecomposable projective right module eR and for any right ideal I, soc(eR/eI) = (eR/eJ)n for some positive integer n.(4) R is right artinian ring and every weakly injective right R-module is weaklyprojective.(5) Every weakly projective right R-module is weakly injective and every weakly injective right R-module is weakly projective.
DOI : 10.4153/CJM-1994-055-9
Mots-clés : 16D40, 16D50, 16L30, 16L60, 16P20 
Jain, S. K.; López-Permouth, S. R.; Oshiro, K.; Saleh, M. A. Weakly Projective and Weakly Injective Modules. Canadian journal of mathematics, Tome 46 (1994) no. 5, pp. 971-981. doi: 10.4153/CJM-1994-055-9
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