Lexsegment ideals are sequentially Cohen-Macaulay (Q2928439)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Lexsegment ideals are sequentially Cohen-Macaulay |
scientific article; zbMATH DE number 6366777
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lexsegment ideals are sequentially Cohen-Macaulay |
scientific article; zbMATH DE number 6366777 |
Statements
7 November 2014
0 references
lexsegment ideals
0 references
primary decomposition
0 references
pretty clean modules
0 references
sequentially Cohen-Macaulay ideals
0 references
Stanley depth
0 references
Lexsegment ideals are sequentially Cohen-Macaulay (English)
0 references
Let \(S=k[x_1,\dots,x_n]\) be the polynomial ring in \(n\) variables over a field \(k\), \(u,v\in S\) be two monomials of degree \(d\geq2\) and \(I=(L(u,v))\) the lexsegment ideal determined by \(u\) and \(v\). The author gives a complete description of the associated primes of lexsegment ideals. His description is given in terms of the support of the monomials \(u\) and \(v\). Moreover, he proves that \(S/I\) is a pretty clean \(S\)-module, therefore \(S/I\) is sequentially Cohen-Macaulay.
0 references
