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Overrings of Bezout Domains

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 [2] Brungs shows that every ring T between a principal (right and left) ideal domain R and its quotient field is a quotient ring of R. In this note we obtain similar results without assuming the ascending chain conditions. For a (right and left) Bezout domain R we show that T is a quotient ring of R which is again a Bezout domain; furthermore Tis a valuation domain if and only if T is a local ring.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 475 - 477
Copyright
Copyright © Canadian Mathematical Society 1973

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. Brungs, H. H., Overrings of principal ideal domains, Proc. Amer. Math. Soc. 28 (1971), 44–46.Google Scholar
3. Cohn, P. M., Noncommutative unique factorization domains, Trans. Amer. Math. Soc. 109 (1963), 313–331.Google Scholar
4. Johnson, R. E., Unique factorization monoids and domains, Proc. Amer. Math. Soc. 28 (1971), 397–404.Google Scholar