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On Inc-Extensions and Polynomials with Unit Content

Published online by Cambridge University Press:  20 November 2018

David E. Dobbs
David E. Dobbs*
Affiliation:
Department of Mathematics, Ayres Hall, University of Tennessee, Knoxville, Tennessee 37916
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Abstract

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It is proved that if u is an element of a faithful algebra over a commutative ring R, then u satisfies a polynomial over R which has unit content if and only if the extension R ⊂ R[u] has the imcomparability property. Applications include new proofs of results of Gilmer-Hoffmann and Papick, as well as a characterization of the P-extensions introduced by Gilmer and Hoffmann.

Keywords

13A1513F0513B2013B25Prime idealp-extensionincomparability propertyintegral closurePriifer domainlying-over propertygoing-up propertycoherent ring
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 1 , 01 March 1980 , pp. 37 - 42
Copyright
Copyright © Canadian Mathematical Society 1980

References

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