Integral closure,basically full closure,and duals of nonresidual closure operations |
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Affiliation: | 1. Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States of America;2. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, United States of America |
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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 [5], 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. |
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Keywords: | Closure operation Test ideal Interior operation Integral closure Basically full Core |
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