Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771785 | Journal of Algebra | 2017 | 12 Pages |
Abstract
Let G be a graph with n vertices and let S=K[x1,â¦,xn] be the polynomial ring in n variables over a field K. Assume that J(G) is the cover ideal of G and J(G)(k) is its k-th symbolic power. We prove that the sequences {sdepth(S/J(G)(k))}k=1â and {sdepth(J(G)(k))}k=1â are non-increasing and hence convergent. Suppose that νo(G) denotes the ordered matching number of G. We show that for every integer kâ¥2νo(G)â1, the modules J(G)(k) and S/J(G)(k) satisfy the Stanley's inequality. We also provide an alternative proof for [9, Theorem 3.4] which states that depth(S/J(G)(k))=nâνo(G)â1, for every integer kâ¥2νo(G)â1.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
S.A. Seyed Fakhari,