Neil Epstein

collaborators

6 papers

math.AC2026

A common framework for test ideals, closure operations, and their duals

Neil Epstein, Rebecca R. G., Janet Vassilev

Closure operations such as tight and integral closure and test ideals have appeared frequently in the study of commutative algebra. This articles serves as a survey of the authors'…

math.AC2026

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.AC2025

An introduction to reciprocal complements of integral domains

Neil Epstein, Lorenzo Guerrieri

Given an integral domain $D$ with fraction field $F$ , its *reciprocal complement* is the subring of $F$ generated by all $1/ d$ for nonzero $d$ in $D$ . This paper serves doubly as a…

math.AC2025

Variants on Frobenius Intersection Flatness and Applications to Tate Algebras

Rankeya Datta, Neil Epstein, Karl Schwede +1

The theory of singularities defined by Frobenius has been extensively developed for $F$ -finite rings and for rings that are essentially of finite type over excellent local rings. H…

math.AG2025

Fundamental algebraic sets and locally unit-additive rings

Neil Epstein

The Fundamental Theorem of Algebra can be thought of as a statement about the real numbers as a space, considered as an algebraic set over the real numbers as a field. This paper i…

math.RA2025

Additive subgroups of a module that are saturated with respect to a subset of the ring

Jesse Elliott, Neil Epstein

Let $T$ be a subset of a ring $A$ , and let $M$ be an $A$ -module. We study the additive subgroups $F$ of $M$ such that, for all $x \in M$ , if $t x \in F$ for some $t \in T$ , then $x…