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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Finiteness conditions for projective and injective modules

Author: Joe W. Fisher
Journal: Proc. Amer. Math. Soc. 40 (1973), 389-394
MSC: Primary 16A50
MathSciNet review: 0335578
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Abstract: Does Hopkins' theorem extend to projective modules, i.e., are projective Artinian modules Noetherian? An example is given to answer this question in the negative; however, we show that the answer is affirmative for certain large classes of projective modules. Dually, are injective Noetherian modules Artinian? Again the answer is negative; nevertheless, we provide an affirmative answer for certain classes of injective modules.

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Keywords: Projective, injective, Artinian, Noetherian, endomorphism rings of modules, semiprimary, P.I.-rings
Article copyright: © Copyright 1973 American Mathematical Society