ON THE OSOFSKY–SMITH THEOREM
2010 ◽
Vol 52
(A)
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pp. 61-67
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AbstractWe 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.
1995 ◽
Vol 52
(3)
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pp. 517-525
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2009 ◽
Vol 321
(5)
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pp. 1538-1545
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1991 ◽
Vol 34
(1)
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pp. 161-166
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Keyword(s):
2014 ◽
Vol 51
(4)
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pp. 547-555
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2016 ◽
Vol 17
(4)
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pp. 979-980
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1980 ◽
Vol 88
(1)
◽
pp. 15-31
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Keyword(s):
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