Author:
Anderson David F.,Arnold Jimmy T.,Dobbs David E.
Abstract
AbstractIt is proved that an integral domain R is a Bézout domain if (and only if) R is integrally closed and I J = {ij|i ∊ I, j ∊ J} for all ideals I and J of R; that is, if (and only if) R is an integrally closed condensed domain. The article then introduces a weakening of the "condensed" concept which, in the context of the k + M construction, is equivalent to a certain field-theoretic condition. Finally, the field extensions satisfying this condition are classified.
Publisher
Canadian Mathematical Society
Cited by
4 articles.
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1. Cramer’s rule over residue class rings of Bézout domains;Linear and Multilinear Algebra;2017-07-11
2. Condensed and Strongly Condensed Domains;Canadian Mathematical Bulletin;2008-09-01
3. Condensed Rings with Zero-Divisors#;Communications in Algebra;2005-10
4. Condensed Domains;Canadian Mathematical Bulletin;2003-03-01