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On Condensed Noetherian Domains Whose Integral Closures are Discrete Valuation Rings

Published online by Cambridge University Press:  20 November 2018

Christian Gottlieb
Christian Gottlieb*
Affiliation:
Department of Mathematics, University of Stockholm, Box 6701, S-113 85 Stockholm, Sweden
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Abstract

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A condensed domain is an integral domain such that IJ = {xy : x ∊ I, y ∊ J } holds for each pair I, J of ideals. We prove that, under suitable conditions, a subring of a discrete valuation ring is condensed if and only if it contains an element of value 2. We also define the concept strongly condensed.

Keywords

13F0513A1513B2013E0513F3013G05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 166 - 168
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Anderson, David F. and Dobbs, David E., On the product of ideals, Canad. Math. Bull. Vol. 26 no 1 (1983).Google Scholar
2. Anderson, David F., Jimmy T. Arnold and David Dobbs, E., Integrally closed condensed domains are Bézout. Canad. Math. Bull. Vol 28 no 1 (1985).Google Scholar