整闭包、基本全封闭、非残留闭包运算的消除
Integral closure, basically full closure, and duals of nonresidual closure operations
摘要：
我们开发了一个对偶操作嵌套对的模块，推广了绝对内部操作和剩余的闭包运算从[ER 21]之间的对偶，扩展我们以前的结果扩展的背景下。我们特别将这种对偶性应用于积分和基本全闭包及其各自的核，以获得积分和基本空的内部及其各自的外壳。我们还对偶一些已知的公式的核心的理想，以获得公式的子模的外壳的内射壳的剩余域。最后给出了数值半群环中的一些例子。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
