Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2025-01-02T18:12:04.277Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Beauregard, R. A., Infinite primes and unique factorization in a principal right ideal domain, Trans. Amer. Math. Soc. 141 (1969), 245-254.Google Scholar
2. Cohn, P. M., Free rings and their relations, Academic Press (London, 1971).Google Scholar
3. Cozzens, J. H., Simple principal left ideal domains, J. Algebra 23 (1972), 66-75.Google Scholar
4. Jacobson, N., Theory of rings, Math. Surveys No. II, Amer. Math. Soc. (1943).Google Scholar
5. Jacobson, N., Structure of rings, Colloq. Publi. Vol. XXXVIII, Amer. Math. Soc. (1964).Google Scholar