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On the Inversion of Right Invariant Elements

Published online by Cambridge University Press:  20 November 2018

Raymond A. Beauregard
Raymond A. Beauregard*
Affiliation:
University of Rhode Island, Kingston, Rhode, Island
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In this note we show that every (not necessarily commutative) integral domain R has a quotient ring which, although need not be a field, has the property that all of its right invariant elements are units. As an application this shows that every PRI (principal right ideal) domain can be embedded in a simple PRI domain which is, in general, not a field.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 289 - 290
Copyright
Copyright © Canadian Mathematical Society 1975

References

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