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Proceedings of the American Mathematical Society

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

 
 

 

Simple maximal quotient rings


Author: Robert A. Rubin
Journal: Proc. Amer. Math. Soc. 55 (1976), 29-32
DOI: https://doi.org/10.1090/S0002-9939-1976-0393097-5
MathSciNet review: 0393097
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Abstract: In this paper we consider the question of when a ring $ \Lambda $ has a simple maximal left ring of quotients. In the first section we determine two necessary conditions; viz. that $ \Lambda $ be left nonsingular, and when $ I$ and $ J$ are nonzero ideals of $ \Lambda $ with $ I \cap J = 0$, then $ I + J$ is not left essential in $ \Lambda $. In the second section we show that these conditions are also sufficient when $ \Lambda $ is of finite left Goldie dimension. In addition, for a left nonsingular ring of finite left Goldie dimension, we determine the ideal structure of the maximal left ring of quotients.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0393097-5
Keywords: Simple ring, nonsingular ring, Goldie dimension, maximal ring of quotients, semisimple ring, self-injective ring
Article copyright: © Copyright 1976 American Mathematical Society

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