Finiteness conditions for projective and injective modules

Fisher, Joe W.

doi:10.1090/S0002-9939-1973-0335578-3

Finiteness conditions for projective and injective modules
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by Joe W. Fisher PDF

Proc. Amer. Math. Soc. 40 (1973), 389-394 Request permission

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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