3 citations · 6 across the 15 of their papers we have counts for
15 papers
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'…
-prereductions, -postexpansions, and related structures
Sarah Poiani, Janet Vassilev
Expanding on the work of Kemp, Ratliff and Shah, for any closure defined on a class of modules over a Noetherian ring, we develop the theory of -prereductions…
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…
Differentially fixed ideals in toric varieties
Lance Edward Miller, William D. Taylor, Janet Vassilev
This article concerns monomial ideals fixed by differential operators of affine semi-group rings over . We give a complete characterization of when this happens. Perhap…
Differential operators, retracts, and toric face rings
Christine Berkesch, C-Y. Jean Chan, Patricia Klein +3
We give explicit descriptions of rings of differential operators of toric face rings in characteristic . For quotients of normal affine semigroup rings by radical monomial ideal…
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…