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Unruly Hilbert Domains

Published online by Cambridge University Press:  20 November 2018

J. L. Mott  and
M. Zafrullah
J. L. Mott
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306
M. Zafrullah
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306
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Abstract

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We give a simple construction of non-Noetherian Hilbert domains whose maximal ideals are all finitely generated. Such domains we call unruly Hilbert domains.

Keywords

13G0513B2013B2513F20Hilbert domainNoetherian domainBezout domainKrull dimension
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 106 - 109
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Brewer, J. and Rutter, E. A., D +M constructions with general overrings, Mich. Math. J. 23 (1976), 33–42.Google Scholar
2. Costa, D., Mott, J. and Zafrullah, M., The construction D +xDs[x], J. Algebra 53 (1978), 423–439.Google Scholar
3. Costa, D., Mott, J. and Zafrullah, M., Overrings and dimensions of general D + M constructions, J. of Nat. Sci. and Math. 26 (1986), 7–14.Google Scholar
4. Gilmer, R. and Heinzer, W., A non-No ether ian two-dimensional Hilbert domain with principal maximal ideals, Mich. Math. J. 23 (1976), 353–362.Google Scholar