Two-sided semisimple maximal quotient rings

Cateforis, Vasily C.

doi:10.1090/S0002-9947-1970-0260801-5

Two-sided semisimple maximal quotient rings
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Trans. Amer. Math. Soc. 149 (1970), 339-349 Request permission

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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