Prime filtrations of monomial ideals and polarizations

被引：43

作者：

Jahan, Ali Soleyman ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fachbereich Math & Informat, D-45117 Essen, Germany

来源：

JOURNAL OF ALGEBRA | 2007年 / 312卷 / 02期

关键词：

prime filtrations; pretty clean modules; Stanley decompositions; multicomplexes;

D O I：

10.1016/j.jalgebra.2006.11.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that an arbitrary monomial ideal I is pretty clean if and only if its polarization I-p is clean. This yields a new characterization of pretty clean monomial ideals in terms of the arithmetic degree, and it also implies that a multicomplex is shellable if and only the simplicial complex corresponding to its polarization is (non-pure) shellable. We also discuss Stanley decompositions in relation to prime filtrations. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1011 / 1032

页数：22

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