5 papers
Generic fiber rings of mixed power series/polynomial rings
William Heinzer, Christel Rotthaus, Sylvia Wiegand
Let K be a field, m and n positive integers, and X = {x_1,...,x_n}, and Y = {y_1,..., y_m} sets of independent variables over K. Let A be the polynomial ring K[X] localized at (X).…
The Gorenstein and complete intersection properties of associated graded rings
William Heinzer, Mee-Kyoung Kim, Bernd Ulrich
Let I be an m-primary ideal of a Noetherian local ring (R,m). We consider the Gorenstein and complete intersection properties of the associated graded ring G(I) and the fiber cone…
Integral closures of ideals in completions of regular local domains
William Heinzer, Christel Rotthaus, Sylvia Wiegand
In this paper we exhibit an example of a three-dimensional regular local domain (A, n) having a height-two prime ideal P with the property that the extension PA^ of P to the n-adic…
Well-centered overrings of an integral domain
William Heinzer, Moshe Roitman
Let A be an integral domain with field of fractions K. We investigate the structure of the overrings B of A (contained in K) that are well-centered on A in the sense that each prin…
A generalized Dedekind-Mertens lemma and its converse
Alberto Corso, William Heinzer, Craig Huneke
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dime…