6 papers
Betti numbers of inductively pierced codes
Hugh Geller, Rebecca R. G., Alexandra Seceleanu +1
Neural ideals were introduced by Curto, Itskov, et al as an algebraic tool to study neural codes. In this paper, we use the notion of polarization introduced by Güntürkün, Jeffries…
The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings
Linquan Ma, Peter M. McDonald, Rebecca R. G. +1
Suppose is an -generated ideal in any ring . We prove a general Briançon-Skoda-type containment relating the integral closure w…
Closure operations induced via resolutions of singularities in characteristic zero
Neil Epstein, Peter M. McDonald, Rebecca R. G. +1
Using the fact that the structure sheaf of a resolution of singularities, or regular alteration, pushes forward to a Cohen-Macaulay complex in equal characteristic zero with a diff…
Rationality for arbitrary closure operations and the test ideal of full extended plus closure
Zhan Jiang, Rebecca R. G
We extend the notion of F-rationality to other closure operations, inspired by the work of Smith, Epstein and Schwede, and Ma and Schwede, which describe F-rationality in terms of…
How to extend closure and interior operations to more modules
Neil Epstein, Rebecca R. G., Janet Vassilev
There are several ways to convert a closure or interior operation to a different operation that has particular desirable properties. In this paper, we axiomatize 3 ways to do so, d…
Cohen-Macaulay test ideals over rings of finite and countable Cohen-Macaulay type
Julian Benali, Shrunal Pothagoni, Rebecca R. G.
The third named author and Pérez proved that under certain conditions the test ideal of a module closure agrees with the trace ideal of the module closure. We use this fact to comp…