Classical quotient rings of PWD's

Author:
Robert Gordon

Journal:
Proc. Amer. Math. Soc. **36** (1972), 39-46

MSC:
Primary 16A08

DOI:
https://doi.org/10.1090/S0002-9939-1972-0309983-4

MathSciNet review:
0309983

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Abstract | References | Similar Articles | Additional Information

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 is right Goldie.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0309983-4

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