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The Ordering of Spec R

Published online by Cambridge University Press:  20 November 2018

William J. Lewis  and
Jack Ohm
William J. Lewis
Affiliation:
University of Nebraska, Lincoln, Nebraska
Jack Ohm
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
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Let Specie denote the set of prime ideals of a commutative ring with identity R, ordered by inclusion; and call a partially ordered set spectral if it is order isomorphic to Spec R for some R. What are some conditions, necessary or sufficient, for a partially ordered set X to be spectral? The most desirable answer would be the type of result that would allow one to stare at the diagram of a given X and then be able to say whether or not X is spectral. For example, it is known that finite partially ordered sets are spectral (see [2] or [5]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 820 - 835
Copyright
Copyright © Canadian Mathematical Society 1976

References

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