Depth of some square free monomial ideals

2012/11/05 by Dorin Popescu, Popescu, Dorin, Andrei Zarojanu +1 · 1 citation
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.1211.0842

openalex publication_date 2012/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I\supsetneq J be two square free monomial ideals of a polynomial algebra over a field generated in degree ≥ 1, resp. ≥ 2 . Almost always when I contains precisely one variable, the other generators having degrees ≥ 2, if the Stanley depth of I/J is ≤ 2 then the usual depth of I/J is ≤ 2 too, that is the Stanley Conjecture holds in these cases.

Citations

• Depth and minimal number of generators of square free monomial ideals
• Stanley conjecture on intersections of four monomial prime ideals

Cited by

• Stanley depth on five generated, squarefree, monomial ideals

Related

• Depth of some special monomial ideals
• Stanley depth on five generated, squarefree, monomial ideals
• Depth of factors of square free monomial ideals
• Depth and minimal number of generators of square free monomial ideals
• Upper bounds for the Stanley depth