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Quotient Rings of Endomorphism Rings of Modules with Zero Singular Submodule

John Hutchinson and Julius Zelmanowitz
Proceedings of the American Mathematical Society
Vol. 35, No. 1 (Sep., 1972), pp. 16-20
DOI: 10.2307/2038429
Stable URL: http://www.jstor.org/stable/2038429
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Quotient Rings of Endomorphism Rings of Modules with Zero Singular Submodule
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Abstract

Throughout this paper $(R, M, N, S)$ will denote a Morita context satisfying a certain nonsingularity condition. For such contexts we give necessary and sufficient conditions in terms of $M$ and $R$ for $S$ to have a semisimple maximal left quotient ring; respectively a full linear maximal left quotient ring, a semisimple classical left quotient ring. In doing so we extend the corresponding well-known theorems for rings (employing them in the process) to endomorphism rings.

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