Prime filtrations of monomial ideals and polarizations

JOURNAL OF ALGEBRA

卷:312

Article

Jahan, Ali Soleyman

关键词: prime filtrations;    pretty clean modules;    Stanley decompositions;    multicomplexes;   

DOI  :  10.1016/j.jalgebra.2006.11.002

来源: Elsevier

【 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.

【 授权许可】

Free