18 citations · 105 across the 29 of their papers we have counts for
6 papers · 2 filters
Zero-divisor graphs of nilpotent-free semigroups
Neil Epstein, Peyman Nasehpour
We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \emph{Armendariz map} betwee…
A dual to tight closure theory
Neil Epstein, Karl Schwede
We introduce an operation on modules over an -finite ring of characteristic . We call this operation \emph{tight interior}. While it exists more generally, in some cases this…
Continuous closure, axes closure, and natural closure
Neil Epstein, Melvin Hochster
Let be a reduced affine -algebra, with corresponding affine algebraic set . Let be the ring of continuous (Euclidean topology) -valued…
A guide to closure operations in commutative algebra
Neil Epstein
This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze st…
Some extensions of Hilbert-Kunz multiplicity
Neil Epstein, Yongwei Yao
Let be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite modul…
Criteria for flatness and injectivity
Neil Epstein, Yongwei Yao
Let be a commutative Noetherian ring. We give criteria for flatness of -modules in terms of associated primes and torsion-freeness of certain tensor products. This allows us…