On an example of Nagarajan
On an example of Nagarajan
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以 Nagarajan 为例
DOI：
10.1016/j.jalgebra.2023.09.038
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发表时间：
2022
影响因子：
0.9
通讯作者：
Anurag Singh
中科院分区：
文献类型：
--
作者：
A. Giokas;Anurag Singh
K. R. Nagarajan 在二阶循环群的作用下，在特征二域上构建了二维形式幂级数环的示例，使得不变量环不是诺特环。我们指出 Nagarajan 的示例如何轻松扩展到每个正素数特征，以及特征零示例：在特征零域上存在一个二维形式幂级数环，具有无限循环群的作用，使得不变量环不是诺特环。正特征和零特征的例子在很多方面都很尖锐。
K. R. Nagarajan constructed an example of a formal power series ring of dimension two, over a field of characteristic two, with the action of a cyclic group of order two, such that the ring of invariants is not noetherian. We point out how Nagarajan's example readily extends to each positive prime characteristic, and also to a characteristic zero example: There exists a formal power series ring of dimension two, over a field of characteristic zero, with an action of the infinite cyclic group, such that the ring of invariants is not noetherian. Both the positive characteristic and the characteristic zero examples are sharp in multiple ways.