Graph and depth of a monomial squarefree ideal

2011/04/29 by Dorin Popescu, Popescu, Dorin
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1104.5596

openalex publication_date 2011/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be a monomial squarefree ideal of a polynomial ring S over a field K such that the sum of every three different of its minimal prime ideals is the maximal ideal of S, or more general a constant ideal. We associate to I a graph on [s], s=|\Min S/I| on which we may \em read the depth of I. In particular, \depth_S I does not depend of char K. Also we show that I satisfies the Stanley's Conjecture.

Citations

• Stanley conjecture on intersections of four monomial prime ideals

Related

• Depth in a pathological case
• Depth and minimal number of generators of square free monomial ideals
• Values and bounds of the Stanley depth
• Depth of factors of square free monomial ideals
• Monomial ideals of minimal depth and trivial modifications