Nakayama闭包、内部操作和核壳对偶
Nakayama closures, interior operations, and core-hull duality
摘要：
利用Epstein和R.G.开发的通道闭合对偶，本文证明了Noether局部环上的Matlis可对偶模类$\mathcal{M}$，当cl是Nakayama闭包且i是其对偶内部时，cl-约化与i-展开之间存在对偶性，从而导致$\mathcal{M}$中模的cl-核与$\mathcal{M}^\vee$中模的i-壳之间存在对偶性.我们进一步表明，许多代数和模块的闭包和内部是中山和描述的方法来计算内部的理想使用闭包和冒号。在完全Gorenstein局部情形下，我们用我们的方法给出了F-合理性与F-正则性、F-内射性与F-纯性的等价性的统一证明。此外，我们还利用$R^{1/p^e}$的映射给出了有限紧闭包检验理想的一个新的刻画。此外，我们还证明了模的可提升积分展度是存在的。
英文摘要：
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 $\mathcal{M}$ 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.
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。
