论文标题
均匀域的水平与接近gorensteinness
Levelness versus nearly Gorensteinness of homogeneous domains
论文作者
论文摘要
水平度和几乎是戈伦斯坦（Gorensteinness）是渐变环的精心研究的特性，作为戈尔伦斯坦（Gorensteinness）的普遍概念。在本文中，我们比较了这些特性的强度。对于任何Cohen-Macaulay均质仿射半群环R，我们为R提供了R-Gorenstein的必要条件，而R r的H-Vector则几乎是Gorenstein，并且我们表明，如果R与Cohen-Macaulay几乎是Gorenstein，则是Cohen-Macaulay 2型2。我们还表明，如果Cohen-Macaulay类型超过2种，则有二维反例。此外，我们表征了低维基型复合物的Stanley-Reisner环的几乎Gorensteinness。
Levelness and nearly Gorensteinness are well-studied properties of graded rings as a generalized notion of Gorensteinness. In this paper, we compare the strength of these properties. For any Cohen-Macaulay homogeneous affine semigroup ring R, we give a necessary condition for R to be non-Gorenstein and nearly Gorenstein in terms of the h-vector of R and we show that if R is nearly Gorenstein with Cohen-Macaulay type 2, then it is level. We also show that if Cohen-Macaulay type is more than 2, there are 2-dimensional counterexamples. Moreover, we characterize nearly Gorensteinness of Stanley-Reisner rings of low-dimensional simplicial complexes.
