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Proceedings of the American Mathematical Society

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



Left Ore principal right ideal domains

Author: Raymond A. Beauregard
Journal: Proc. Amer. Math. Soc. 102 (1988), 459-462
MSC: Primary 16A02
MathSciNet review: 928960
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Abstract: The rings referred to in the title of this paper have long been conjectured to be principal left ideal domains. In a recent paper [6] Cohn and Schofield have produced examples (of simple rings) showing that this is not the case. As a result, interest in this type of ring has deepened (see [5], for example, where these rings are referred to as right principal Bezout domains). Our main purpose here is to prove that such rings are either principal left ideal domains or left and right primitive rings.

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Keywords: Principal ideal domain, Ore domain, Bezout domain, invariant element, bounded element, primitive ring
Article copyright: © Copyright 1988 American Mathematical Society

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