The diagonal subring and the Cohen-Macaulay property of a multigraded ring
The diagonal subring and the Cohen-Macaulay property of a multigraded ring
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多级环的对角子环和 Cohen-Macaulay 性质
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发表时间：
1999
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通讯作者：
Eero Hyry
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作者：
Eero Hyry
设T是定义在局部环（A，m）上的重分次环.本文讨论T的Cohen-Macaulay性质与对角子环T的Cohen-Macaulay性质之间的关系。在双分次情形下，我们能够给出T的Cohen-Macaulay性的充分必要条件。如果I1，. . .，Ir ∈ A是正高度理想，我们可以比较多Rees代数RA（I1，. . .，Ir）具有通常的Rees代数RA（I1 · · · Ir）的CohenMacaulay性质.在多Rees代数是Cohen-Macaulay的情形下，我们还得到了两个m-准素理想的联合约化数的一个界.
Let T be a multigraded ring defined over a local ring (A, m). This paper deals with the question how the Cohen-Macaulay property of T is related to that of its diagonal subring T∆. In the bigraded case we are able to give necessary and sufficient conditions for the Cohen-Macaulayness of T . If I1, . . . , Ir ⊂ A are ideals of positive height, we can then compare the CohenMacaulay property of the multi-Rees algebra RA(I1, . . . , Ir) with the CohenMacaulay property of the usual Rees algebra RA(I1 · · · Ir). We also obtain a bound for the joint reduction numbers of two m-primary ideals in the case the corresponding multi-Rees algebra is Cohen-Macaulay.