# A dual to tight closure theory

@article{Epstein2014ADT, title={A dual to tight closure theory}, author={Neil M. Epstein and Karl Schwede}, journal={Nagoya Mathematical Journal}, year={2014}, volume={213}, pages={41 - 75} }

Abstract We introduce an operation on modules over an F-finite ring of characteristic p. We call this operation tight interior. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight closure. Moreover, the interior of the ring itself is simply the big test ideal. We directly prove, without appeal to tight closure, results analogous to persistence, colon capturing, and working modulo minimal primes, and we begin to develop a theory dual to phantom…

## 4 Citations

Nakayama closures, interior operations, and core-hull duality.

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Exploiting the interior-closure duality developed by Epstein and R.G., we show that for the class of Matlis dualizable modules $\mathcal{M}$ over a Noetherian local ring, when cl is a Nakayama…

Characterizing F-rationality of Cohen-Macaulay Rings via Canonical Modules

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- 2018

This dissertation investigates the characterization of F -rationality. Much work has been done to characterize F -rationality. Here, we will assume that the underlying ring is commutative and…

Closure-interior duality over complete local rings

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- 2019

We define a duality operation connecting closure operations, interior operations, and test ideals, and describe how the duality acts on common constructions such as trace, torsion, tight and integral…

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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], extending our previous…

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