论文标题
在Nagarajan的例子
On an example of Nagarajan
论文作者
论文摘要
K. R. Nagarajan构建了一个尺寸二维形式的尺寸的形式功率系列环的示例，在一个特征性的两个领域，其循环阶二的作用是不变的，因此不变的环。我们指出，Nagarajan的示例如何容易地扩展到每个正质量特征，也可以延伸到一个特征零示例：在特征零的领域中，存在一个正式的功率系列环，并具有无限环状群的作用，因此，不变的环不是不可分割的。积极特征和特征零示例都以多种方式敏锐。
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.
