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Right Quotient Rings of a Right LCM Domain

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 paper we continue our investigation of the class of right LCM domains which was introduced in [2]. A right LCM domain is an (not necessarily commutative) integral domain with unity in which the intersection of any two principal right ideals is again principal. In this note we study the right quotient rings of such a ring. In Section 1 we describe some of the characteristic properties of right quotient monoids with respect to which quotient rings are formed. Three particular types of quotient rings are described in Section 2. In Section 3 we relate the right ideals of a ring to those of its quotient ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 983 - 988
Copyright
Copyright © Canadian Mathematical Society 1972

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. Beauregard, R. A., Right LCM domains, Proc. Amer. Math. Soc. 30 (1971), 1–7.Google Scholar
3. Brungs, H. H., Ringe mit eindeutiger Faktorzerlegung, J. Reine Angew. Math. 236 (1969), 43–66.Google Scholar
4. Jacobson, N., The theory of rings, Math. Surveys No. II, Amer. Math. Soc., 1943.Google Scholar