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Proceedings of the American Mathematical Society

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

 

 

Left perfect rings that are right perfect and a characterization of Steinitz rings


Author: William H. Rant
Journal: Proc. Amer. Math. Soc. 32 (1972), 81-84
MSC: Primary 16.50
MathSciNet review: 0289571
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Abstract: A proof is given to show all flat left modules of a ring are free if and only if the ring is a local ring with a left T-nilpotent maximal ideal. We characterize left perfect rings whose radical R has the property that $ I{R^n} = \{ 0\} $ for some positive integer n if I is a finitely generated right ideal contained in R. We cite an example of a left perfect ring which does not have this property. It is shown that if the set of irreducible elements of a left perfect ring is right T-nilpotent then the ring is right perfect.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0289571-9
Keywords: Perfect ring, Steinitz ring, T-nilpotent, local ring, radical, irreducible element
Article copyright: © Copyright 1972 American Mathematical Society