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Pairs of Rings with the Same Prime Ideals, II

Published online by Cambridge University Press:  20 November 2018

David F. Anderson  and
David E. Dobbs
David F. Anderson
Affiliation:
University of Tennessee, Knoxville, Tennessee
David E. Dobbs
Affiliation:
University of Tennessee, Knoxville, Tennessee
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Much of [2] was devoted to studying pairs of subrings A ⊂ B of a field with the property that A and B have the same prime ideals. In this paper, we continue that investigation, but we no longer assume that A and B are comparable. Interestingly, most of the results of [2] carry over to this more general context. Besides such extensions of [2], additional motivation for the more general context comes from the need to explicate some naturally occurring examples (see Examples 2.5, 3.6, and 4.3).

Section 2 begins by showing that we may reduce to the case in which R is a quasilocal domain with nonzero maximal ideal M and quotient field K. Proposition 2.3 establishes that the set C(R) of all subrings A of K with Spec(A) = Spec(R) forms a complete semilattice.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1399 - 1409
Copyright
Copyright © Canadian Mathematical Society 1988

References

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