18 citations · 105 across the 29 of their papers we have counts for
39 papers · 1 filter
Rings where a non-nilpotent sum of units is a unit
Neil Epstein, Jay Shapiro
A ring is *unit-additive* if a sum of units is always either a unit or nilpotent. For example, and are unit-additive, but is not. We prove a wide-ra…
Mittag-Leffler modules and variants on intersection flatness
Rankeya Datta, Neil Epstein, Kevin Tucker
We systematically study the intersection flatness and Ohm-Rush properties for modules over a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and…
Rings that are Egyptian with respect to a multiplicative set
Neil Epstein
The notion of an \emph{Egyptian} integral domain (where every fraction can be written as a sum of unit fractions with denominators from ) is extended here to the notion that…
Egyptian integral domains
Neil Epstein
The notion of an Egyptian domain (where the analogue of Egyptian fractions works appropriately), first explored by Guerrieri-Loper-Oman, is extended to the more general notions of…
On posets, monomial ideals, Gorenstein ideals and their combinatorics
Geir Agnarsson, Neil Epstein
In this article we first compare the set of elements in the socle of an ideal of a polynomial algebra over a field that are not in the ideal itself and Maca…
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…