Monomial Ideals under Ideal Operations
Monomial Ideals under Ideal Operations
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理想运算下的单项式理想
DOI：
10.1080/00927872.2014.952012
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发表时间：
2013
影响因子：
0.7
通讯作者：
Tongsuo Wu
中科院分区：
文献类型：
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作者：
Jin Guo;Tongsuo Wu
在本文中，我们证明了对于K[x 1， x 2，…，x n]的单项式理想I，如果I具有相同的性质，则积分闭包是Borel型单项式理想（分别为Borel-fixed，强稳定，lexsegment，或universal lexsegment）。我们还证明了I的第k次符号幂I (k)保持Borel型、Borel固定和强稳定的性质，如果I是稳定的lexsegment，则I (k)是lexsegment。对于单项式理想I和单项式素数理想P，研究了一个新的理想J(I， P)，并给出了I (k)初等分解的清晰描述。然后定义了单项理想J的一个新的简单复形J Δ，并证明了。最后，在一个附加的弱假设下，我们证明了当且仅当单项式理想的极化是无平方强稳定理想时，单项式理想是全称lexsegment。
In this article, we show for a monomial ideal I of K[x 1, x 2,…, x n ] that the integral closure is a monomial ideal of Borel type (Borel-fixed, strongly stable, lexsegment, or universal lexsegment respectively), if I has the same property. We also show that the kth symbolic power I (k) of I preserves the properties of Borel type, Borel-fixed and strongly stable, and I (k) is lexsegment if I is stably lexsegment. For a monomial ideal I and a monomial prime ideal P, a new ideal J(I, P) is studied, which also gives a clear description of the primary decomposition of I (k). Then a new simplicial complex J Δ of a monomial ideal J is defined, and it is shown that . Finally, we show under an additional weak assumption that a monomial ideal is universal lexsegment if and only if its polarization is a squarefree strongly stable ideal.
DOI：
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发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
--
作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest