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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Classical quotient rings of PWD's


Author: Robert Gordon
Journal: Proc. Amer. Math. Soc. 36 (1972), 39-46
MSC: Primary 16A08
MathSciNet review: 0309983
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Abstract: Piecewise domains which are right orders in semiprimary rings are characterized. An example is given showing the result obtained is ``best possible". A further example is obtained of a prime right Goldie ring possessing a regular element which becomes a left zero divisor in some prime overring. This example leads to the construction of a PWD R not satisfying the regularity condition, but for which $ R/N(R)$ is right Goldie.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0309983-4
PII: S 0002-9939(1972)0309983-4
Keywords: Piecewise domain, essentiality condition, exhaustive set, order, classical quotient ring, Goldie ring, principal right ideals projective, torsion-free, left regularity condition, Ore domain, linear equations
Article copyright: © Copyright 1972 American Mathematical Society