论文标题
规范模块的痕迹，Ext的歼灭器和接近Gorenstein的环类
Trace of canonical modules, annihilator of Ext, and classes of rings close to being Gorenstein
论文作者
论文摘要
在本说明中，我们研究了经典模块的理想。给出了痕量理想的特征，从某些EXT模块的歼灭者角度来看。我们将结果应用于研究最近出现在最近文献中的戈伦斯坦（Gorenstein）的许多类别。我们讨论了赫尔佐格·史蒂姆（Herzog-Hibi-Stamate）引入的几乎戈伦斯坦内斯（Gorensteinness）的行为，并在常规序列减少下。提出了几乎Gorenstein版本的Tachikawa猜想，并为2型环提供了肯定的答案。我们还使用规范模块介绍了几乎薄弱的戈伦斯坦环类，并表明它们几乎是戈伦斯坦环在维度上，并且与Artinian情况下的Teter环密切相关。我们解释了它们的基本属性并举例说明。
In this note we study trace ideals of canonical modules. Characterizations of the trace ideals in terms of annihilators of certain Ext modules are given. We apply our results to study many classes of rings close to being Gorenstein that appear in recent literature. We discuss the behavior of nearly Gorensteinness, introduced by Herzog-Hibi-Stamate, under reductions by regular sequences. A nearly Gorenstein version of the Tachikawa conjecture is posed, and an affirmative answer given for type 2 rings. We also introduce the class of weakly almost Gorenstein rings using the canonical module, and show that they are almost Gorenstein rings in dimension one, and are closely related to Teter rings in the artinian case. We explain their basic properties and give some examples.
