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Integrally Closed Condensed Domains are Bézout

Published online by Cambridge University Press:  20 November 2018

David F. Anderson ,
Jimmy T. Arnold  and
David E. Dobbs
David F. Anderson
Affiliation:
Department of Mathematics, University of Tennessee Knoxville, Tennessee 37996-1300 U.S.A.
Jimmy T. Arnold
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and, State University Blacksburg, Virginia 24061 U.S.A.
David E. Dobbs
Affiliation:
Department of Mathematics, University of Tennessee Knoxville, Tennessee 37996-1300 U.S.A.
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Abstract

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It 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.

Keywords

13F0513A1513G0513E0512F10

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 1 , 01 March 1985 , pp. 98 - 102
Copyright
Copyright © Canadian Mathematical Society 1985

References

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