Quotient rings of endomorphism rings of modules with zero singular submodule

Hutchinson, John; Zelmanowitz, Julius

doi:10.1090/S0002-9939-1972-0297805-X

Quotient rings of endomorphism rings of modules with zero singular submodule
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Proc. Amer. Math. Soc. 35 (1972), 16-20 Request permission

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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