Notes on C-Graded Modules Over an Affine Semigroup Ring K[C]
Notes on C-Graded Modules Over an Affine Semigroup Ring K[C]
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DOI：
10.1080/00927870802104295
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发表时间：
2005-06
影响因子：
0.7
通讯作者：
Kohji Yanagawa
中科院分区：
文献类型：
--
作者：
Kohji Yanagawa
设 C ⊂ ℕ d 为仿射半群，R = K[C] 为其半群环。本文是关于“C 级”R 模 M = ⨁ c∈C M c 的各种结果的集合，特别是 R 的单项式理想。例如，我们展示以下内容：如果 R 是正规的且 I ⊂ R 是激进单项式理想（即 R/I 是 Stanley–Reisner 环的推广），则 R/I 的顺序 Cohen–Macaulay 性质是“几何实现”的拓扑性质此外，我们可以给出该结果的无方形模块/可构造滑轮版本。我们还证明，如果 R 是正规的且 I ⊂ R 是 Cohen-Macaulay 单项式理想，则又是 Cohen-Macaulay。
Let C ⊂ ℕ d be an affine semigroup, and R = K[C] its semigroup ring. This article is a collection of various results on “C-graded” R-modules M = ⨁ c∈C M c , especially, monomial ideals of R. For example, we show the following: If R is normal and I ⊂ R is a radical monomial ideal (i.e., R/I is a generalization of Stanley–Reisner rings), then the sequentially Cohen–Macaulay property of R/I is a topological property of the “geometric realization” of the cell complex associated with I. Moreover, we can give a squarefree modules/constructible sheaves version of this result. We also show that if R is normal and I ⊂ R is a Cohen–Macaulay monomial ideal, then is Cohen–Macaulay again.