Depth of factors of square free monomial ideals

2011/10/10 by Dorin Popescu, Popescu, Dorin · 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.1110.1963

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

Abstract

Let I be an ideal of a polynomial algebra over a field, generated by r square free monomials of degree d. If r is bigger (or equal, if I is not principal) than the number of square free monomials of I of degree d+1, then \depth_SI= d. Let J\subsetneq I, J\not =0 be generated by square free monomials of degree ≥ d+1. If r is bigger than the number of square free monomials of I∖ J of degree d+1, or more generally the Stanley depth of I/J is d, then \depth_SI/J= d. In particular, Stanley's Conjecture holds in theses cases.

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