Rebecca R. G.

activity

20152026

most citedClosure operations that induce big Cohen-Macaulay modules and classification of singularities

12 citations · 17 across the 10 of their papers we have counts for

collaborators

11 papers

math.AC2026

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…

math.AC2025

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 $J = (f_{1}, \dots, f_{n})$ is an $n$ -generated ideal in any ring $R$ . We prove a general Briançon-Skoda-type containment relating the integral closure $J^{n + k - 1}$ w…

math.AC2025

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…

math.AC2023

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…

math.AC2023

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…

math.AC2021

Integral closure, basically full closure, and duals of nonresidual closure operations

Neil Epstein, Rebecca R. G., Janet Vassilev

We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [ER21], extend…

math.AC2021

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…

math.AC2016★ 2 cited

Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts

Geoffrey D. Dietz, Rebecca R. G

Let $R$ be a commutative, local, Noetherian ring. In a past article, the first author developed a theory of $R$ -algebras, termed seeds, that can be mapped to balanced big Cohen-Mac…

math.AC2016★ 1 cited

$F$ -singularities under generic linkage

Linquan Ma, Janet Page, Rebecca R. G. +2

Let $R = k [x_{1}, \dots, x_{n}]$ be a polynomial ring over a prefect field of positive characteristic. Let $I$ be an unmixed ideal in $R$ and let $J$ be a generic link of $I$ in $S=R[u_{ij…

math.AC2015★ 2 cited

Closure operations that induce big Cohen-Macaulay algebras

Rebecca R. G

We study closure operations over a local domain R that satisfy a set of axioms introduced by Geoffrey Dietz. The existence of a closure operation satisfying the axioms (called a Di…

math.AC2015★ 12 cited

Closure operations that induce big Cohen-Macaulay modules and classification of singularities