Geodesic
ON THE OSOFSKY–SMITH THEOREM*
Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 61-67

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

We recall a version of the Osofsky–Smith theorem in the context of a Grothendieck category and derive several consequences of this result. For example, it is deduced that every locally finitely generated Grothendieck category with a family of completely injective finitely generated generators is semi-simple. We also discuss the torsion-theoretic version of the classical Osofsky theorem which characterizes semi-simple rings as those rings whose every cyclic module is injective.
DOI : 10.1017/S0017089510000169
Mots-clés : 16D50, 16S90 
CRIVEI, SEPTIMIU; NĂSTĂSESCU, CONSTANTIN; TORRECILLAS, BLAS. ON THE OSOFSKY–SMITH THEOREM*. Glasgow mathematical journal, Tome 52 (2010) no. A, pp. 61-67. doi: 10.1017/S0017089510000169
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