论文标题
参数系统和cohen--macaulay属性
Systems of parameters and the Cohen--Macaulay property
论文作者
论文摘要
我们回想起与参数系统相关的Cohen--Macaulayness的数值标准，并引入了König类型的单一理想，其中包括König图的边缘理想。我们表明，当且仅当其相应的残基类环允许其元素为$ x_i-x_j $的元素的参数系统时，单一理想是König类型的。这提供了科尼格图的代数表征。我们使用此特殊的参数系统来研究König图的边缘理想以及对某些POSET家族的阶级复合物的研究。最后，对于任何简单的复合物$δ$，我们引入了具有通用构造原理的$ k [δ] $的参数系统，独立于基础场，仅取决于$δ$的面。这种参数系统是测试cohen-史坦利 - 简单复合物的Reisner环的有效工具。
We recall a numerical criteria for Cohen--Macaulayness related to system of parameters, and introduce monomial ideals of König type which include the edge ideals of König graphs. We show that a monomial ideal is of König type if and only if its corresponding residue class ring admits a system of parameters whose elements are of the form $x_i-x_j$. This provides an algebraic characterization of König graphs. We use this special parameter systems for the study of the edge ideal of König graphs and the study of the order complex of a certain family of posets. Finally, for any simplicial complex $Δ$ we introduce a system of parameters for $K[Δ]$ with a universal construction principle, independent of the base field and only dependent on the faces of $Δ$. This system of parameters is an efficient tool to test Cohen--Macaulayness of the Stanley--Reisner ring of a simplicial complex.
