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6 papers · 2 filters
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…
The structure of the core of ideals
Alberto Corso, Claudia Polini, Bernd Ulrich
The core of an -ideal is the intersection of all reductions of . This object was introduced by D. Rees and J. Sally and later studied by C. Huneke and I. Swanson, who sho…
On residually S_2 ideals and projective dimension one modules
Alberto Corso, Claudia Polini
We prove that certain modules are faithful. This enables us to draw consequences about the reduction number and the integral closure of some classes of ideals.
Strongly Cohen-Macaulay ideals of small second analytic deviation
Alberto Corso, Claudia Polini
We characterize the strongly Cohen-Macaulay ideals of second analytic deviation one in terms of depth properties of the powers of the ideal in the `standard range.' This provides a…