Integral closure, basically full closure, and duals of nonresidual closure operations
Commutative Algebra
2022-09-02 v2
Abstract
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 results to the expanded context. We apply this duality in particular to integral and basically full closures and their respective cores to obtain integral and basically empty interiors and their respective hulls. We also dualize some of the known formulas for the core of an ideal to obtain formulas for the hull of a submodule of the injective hull of the residue field. The article concludes with illustrative examples in a numerical semigroup ring.
Keywords
Cite
@article{arxiv.2109.08772,
title = {Integral closure, basically full closure, and duals of nonresidual closure operations},
author = {Neil Epstein and Rebecca R. G. and Janet Vassilev},
journal= {arXiv preprint arXiv:2109.08772},
year = {2022}
}
Comments
Edited for readability and clarity. 39 pages, to appear in J. Pure Appl. Algebra