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- National Superconducting Cyclotron LaboratoryUS60 papers
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9 papers · 1 filter
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).…
Independence of the total reflexivity conditions for modules
David Jorgensen, Liana Sega
We show that the conditions defining total reflexivity for modules are independent. In particular, we construct a commutative Noetherian local ring and a reflexive -module $…
Open loci of graded modules
Christel Rotthaus, Liana M. Sega
Let $A=\oplus_{i\in \nn}A_i$ be an excellent homogeneous Noetherian graded ring and let $M=\oplus_{n\in \zz}M_n$ be a finitely generated graded -module. We consider as a mod…
Sally modules and associated graded rings
Alberto Corso, Claudia Polini, Maria Vaz Pinto
We study the depth properties of the associated graded ring of an m-primary ideal I in terms of numerical data attached to the ideal I. We also find bounds on the Hilbert coefficie…
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…
Core and residual intersections of ideals
Alberto Corso, Claudia Polini, Bernd Ulrich
D. Rees and J. Sally defined the core of an -ideal as the intersection of all minimal reductions of . However, it is not easy to give an explicit characterization o…