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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The structure of rings with faithful nonsingular modules


Author: J. M. Zelmanowitz
Journal: Trans. Amer. Math. Soc. 278 (1983), 347-359
MSC: Primary 16A48; Secondary 16A08, 16A42, 16A53, 16A64, 16A65
MathSciNet review: 697079
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Abstract: It is shown that the existence of a faithful nonsingular uniform module characterizes rings which have a full linear maximal quotient ring. New information about the structure of these rings is obtained and their maximal quotient rings are constructed in an explicit manner. More generally, rings whose maximal quotient rings are finite direct sums of full linear rings are characterized by the existence of a faithful nonsingular finite dimensional module.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0697079-3
PII: S 0002-9947(1983)0697079-3
Article copyright: © Copyright 1983 American Mathematical Society