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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Left versus right LCM domains


Author: Raymond A. Beauregard
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0556612-5
Keywords: Right LCM domain, left-right symmetry, intervals of principal right ideals, (left) Ore condition
Article copyright: © Copyright 1980 American Mathematical Society