论文标题
在广义的戈伦斯坦本地环上
On generalized Gorenstein local rings
论文作者
论文摘要
在本文中，我们引入了广义的Gorenstein Local（GGL）环。 GGL环的概念是几乎Gorenstein环的概念的自然概括，因此可以将其视为GGL环理论的一部分。对于Cohen-Macaulay本地环$ r $，我们探讨了最大理想的内态代数，规范模块，Ulrich理想和与GGL属性相关的参数理想的Rees代数的追踪理想。我们还提供了许多矩阵的数值半群环，理想化和确定环的示例。
In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a Cohen-Macaulay local ring $R$, we explore the endomorphism algebra of the maximal ideal, the trace ideal of the canonical module, Ulrich ideals, and Rees algebras of parameter ideals in connection with the GGL property. We also give numerous examples of numerical semigroup rings, idealizations, and determinantal rings of certain matrices.
