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

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DOI

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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     title = {ON {THE} {OSOFSKY{\textendash}SMITH} {THEOREM*}},
     journal = {Glasgow mathematical journal},
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     year = {2010},
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     doi = {10.1017/S0017089510000169},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000169/}
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