论文标题
nakayama封闭，室内操作和核心双重性
Nakayama closures, interior operations, and core-hull duality
论文作者
论文摘要
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 closure and i its dual interior, there is a duality between cl-reductions and i-expansions that leads to a duality between the cl-core of modules in $ \ mathcal {m} $和$ \ Mathcal {m}^\ vee $中的模块i-hull。我们进一步表明，许多代数和模块封闭和内饰都是中山山，并描述了一种使用封闭和结肠来计算理想内部的方法。我们使用我们的方法在完整的戈伦斯坦本地情况下，给出了F理性与F型的等效性和F型f式的统一证明。此外，我们从$ r^{1/p^e} $的地图方面给出了有限性紧密闭合测试的新特征。此外，我们证明了一个模块的可启动积分传播。
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 closure and i its dual interior, there is a duality between cl-reductions and i-expansions that leads to a duality between the cl-core of modules in $\mathcal{M}$ and the i-hull of modules in $\mathcal{M}^\vee$. We further show that many algebra and module closures and interiors are Nakayama and describe a method to compute the interior of ideals using closures and colons. We use our methods to give a unified proof of the equivalence of F-rationality with F-regularity, and of F-injectivity with F-purity, in the complete Gorenstein local case. Additionally, we give a new characterization of the finitistic tight closure test ideal in terms of maps from $R^{1/p^e}$. Moreover, we show that the liftable integral spread of a module exists.
