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Proceedings of the American Mathematical Society

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

 

 

Some examples from infinite matrix rings


Authors: Robert W. Miller and Darrel R. Turnidge
Journal: Proc. Amer. Math. Soc. 38 (1973), 65-67
DOI: https://doi.org/10.1090/S0002-9939-1973-0310001-3
MathSciNet review: 0310001
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Abstract: Examples are given of the following: (1) an injective Noetherian right module which is not Artinian, (2) a linearly compact Noetherian right module over a right perfect ring which is not Artinian, and (3) a (linearly compact) Artinian left module over a right perfect ring which is not Noetherian. These examples answer questions posed by J. W. Fisher and F. L Sandomierski in the Proceedings of the Utah Conference on Ring Theory held in 1971.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310001-3
Keywords: Injective modules with chain conditions, linearly compact modules with chain conditions, perfect rings
Article copyright: © Copyright 1973 American Mathematical Society