11 citations · 17 across the 5 of their papers we have counts for
9 papers
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…
The Ohm-Rush content function III: Completion, globalization, and power-content algebras
Neil Epstein, Jay Shapiro
One says that a ring homomorphism is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element , there is a…
Gaussian elements of a semicontent algebra
Neil Epstein, Jay Shapiro
The connection between a univariate polynomial having locally principal content and the content function acting like a homomorphism (the so-called Gaussian property) has been explo…
The Ohm-Rush content function II. Noetherian rings, valuation domains, and base change
Neil Epstein, Jay Shapiro
The notion of an Ohm-Rush algebra, and its associated content map, has connections with prime characteristic algebra, polynomial extensions, and the Ananyan-Hochster proof of Still…
Perinormality in pullbacks
Neil Epstein, Jay Shapiro
We further develop the notion of perinormality from our last paper, showing that it is preserved by many pullback constructions. In doing so, we introduce the concepts of relative…
Perinormality -- a generalization of Krull domains
Neil Epstein, Jay Shapiro
We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the clas…
The Ohm-Rush content function
Neil Epstein, Jay Shapiro
The content of a polynomial over a ring is a well understood notion. Ohm and Rush generalized this concept of a content map to an arbitrary ring extension of , although it c…
A Dedekind-Mertens theorem for power series rings
Neil Epstein, Jay Shapiro
We prove a power series ring analogue of the Dedekind-Mertens lemma. Along the way, we give limiting counterexamples, we note an application to integrality, and we correct an error…
Strong Krull primes and flat modules
Neil Epstein, Jay Shapiro
There are several theorems describing the intricate relationship between flatness and associated primes over commutative Noetherian rings. However, associated primes are known to a…