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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Two-sided semisimple maximal quotient rings

Author: Vasily C. Cateforis
Journal: Trans. Amer. Math. Soc. 149 (1970), 339-349
MSC: Primary 16.80
MathSciNet review: 0260801
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Abstract: Let R be an associative ring with singular right ideal zero and finite right Goldie dimension; F. L. Sandomierski has shown that the (R. E. Johnson) maximal right quotient ring Q of R is then semisimple (artinian). In this paper necessary and sufficient conditions are sought that Q be also a left (necessarily the maximal) quotient ring of R. Flatness of Q as a right R-module is shown to be such a condition. The condition that R have singular left ideal zero and finite left Goldie dimension, though necessary, is shown to be not sufficient in general. Conditions of two-sidedness of Q are also obtained in terms of the homogeneous components (simple subrings) of Q and the subrings of R, they induce.

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Keywords: Singular right ideal, Goldie dimension, maximal right quotient ring, classical right quotient ring, injective hull of a module, flat module, tensor product of modules, semisimple artinian ring, von Neumann regular ring
Article copyright: © Copyright 1970 American Mathematical Society