论文标题
在无限生成的弗罗贝尼乌斯代数的基因座上
On the infinitely generated locus of Frobenius algebras of rings of prime characteristic
论文作者
论文摘要
让$ r $成为一个值得交付的Noetherian圆环。本文的主要目的是在\ [\ [\ [w^r}：= \ {\ Mathfrak {\ Mathfrak {p} \ in \ operatorName {spec}（r）：\ \ \ m athcal {f}^e _ { pice} \} \]是Zariski拓扑中的一个开放集，其中$ \ MATHCAL {f}^{e _ {\ Mathfrak {\ Mathfrak {p}}} $表示frobenius代数附加在$ r _ {$ r _}的$ r _ {$ nirs $ whull的$ r _ {$ wer $ whull的$ r _} $ whull $ _} $ whull的$ _} $ wer $ whull $ whull $ wers $ whull wer $ whull wer $ wers $ whull。斯坦利 - Reisner Ring；此外，在这种情况下，我们明确计算其封闭的补充，提供了这样做的算法方法。
Let $R$ be a commutative Noetherian ring of prime characteristic $p$. The main goal of this paper is to study in some detail when \[ \overline{W^R}:=\{\mathfrak{p}\in\operatorname{Spec} (R):\ \mathcal{F}^{E_{\mathfrak{p}}}\text{ is finitely generated as a ring over its degree zero piece}\} \] is an open set in the Zariski topology, where $\mathcal{F}^{E_{\mathfrak{p}}}$ denotes the Frobenius algebra attached to the injective hull of the residue field of $R_{\mathfrak{p}}.$ We show that this is true when $R$ is a Stanley--Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.
