论文标题
规范理想的减少数量
The reduction number of canonical ideals
论文作者
论文摘要
在本文中，我们介绍了Cohen-Macaulay本地环的不变，从规范理想的减少来看。不变的可以在任意的Cohen-Macaulay环中定义，并衡量与Gorenstein的近距离。首先，我们通过在维度一中使用不变性，阐明了几乎戈伦斯坦环与几乎戈伦斯坦环之间的关系。接下来，我们是根据不变的痕迹理想对戈伦斯坦环的理想化。它为几乎戈伦斯坦的理想化特性提供了更好的前景。
In this paper, we introduce an invariant of Cohen-Macaulay local rings in terms of the reduction number of canonical ideals. The invariant can be defined in arbitrary Cohen-Macaulay rings and it measures how close to being Gorenstein. First, we clarify the relation between almost Gorenstein rings and nearly Gorenstein rings by using the invariant in dimension one. We next characterize the idealization of trace ideals over Gorenstein rings in terms of the invariant. It provides better prospects for a result of the almost Gorenstein property of idealization.
