Left versus right LCM domains
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- by Raymond A. Beauregard PDF
- Proc. Amer. Math. Soc. 78 (1980), 464-466 Request permission
Abstract:
It is well known that every right Bezout domain satisfying the left Ore (multiple) condition is a left Bezout domain. A similar statement for the smaller class of principal right ideal domains is a long-standing conjecture which remains unresolved. In this paper we settle the analogous question for the larger class of right LCM domains.References
- Raymond A. Beauregard, Right $\textrm {LCM}$ domains, Proc. Amer. Math. Soc. 30 (1971), 1β7. MR 279125, DOI 10.1090/S0002-9939-1971-0279125-1
- Raymond A. Beauregard, Left and right invariance in an integral domain, Proc. Amer. Math. Soc. 67 (1977), no.Β 2, 201β205. MR 457480, DOI 10.1090/S0002-9939-1977-0457480-2
- P. M. Cohn, Free rings and their relations, London Mathematical Society Monographs, No. 2, Academic Press, London-New York, 1971. MR 0371938
- Arun Vinayak Jategaonkar, Left principal ideal domains, J. Algebra 8 (1968), 148β155. MR 218387, DOI 10.1016/0021-8693(68)90040-9
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 464-466
- MSC: Primary 16A06
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556612-5
- MathSciNet review: 556612