AI 中文总结
研究二维正则局部环上与理想相关的爆破代数（里斯代数、扩展里斯代数和相伴分次环）的近戈伦斯坦性质，通过扩展框架建立刻画及关系，得到整闭理想的完全分类。
AI 中文摘要
本文略微扩展了由赫尔佐格 - 日比 - 斯塔马特引入的近戈伦斯坦分次环的框架，研究了与理想相关的爆破代数的近戈伦斯坦性质，即里斯代数、扩展里斯代数和相伴分次环。我们建立了这些代数近戈伦斯坦性质的刻画并阐明它们之间的关系。特别地，对于二维正则局部环，我们得到了使这些爆破代数为近戈伦斯坦的整闭理想的完全分类。
英文摘要
In this paper, we slightly extend the framework of nearly Gorenstein graded rings introduced by Herzog-Hibi-Stamate, and investigate the nearly Gorenstein property of the blow-up algebras associated with an ideal, namely the Rees algebra, the extended Rees algebra, and the associated graded ring. We establish characterizations of the nearly Gorenstein property for these algebras and clarify the relations among them. In particular, for two-dimensional regular local rings, we obtain a complete classification of the integrally closed ideals for which these blow-up algebras are nearly Gorenstein.
Comments21 pages
