On Inc-Extensions and Polynomials with Unit Content

Abstract

AbstractIt 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.