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Simple Maximal Quotient Rings

Robert A. Rubin
Proceedings of the American Mathematical Society
Vol. 55, No. 1 (Feb., 1976), pp. 29-32
DOI: 10.2307/2041834
Stable URL: http://www.jstor.org/stable/2041834
Page Count: 4
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Simple Maximal Quotient Rings
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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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