Monomial ideals of minimal depth and trivial modifications

2012/03/15 by Muhammad Ishaq, Ishaq, Muhammad
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.1203.3319

openalex publication_date 2012/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley's conjecture holds for these ideals. Also we show that if Stanley's conjecture holds for a square free monomial ideal then it holds for all its trivial modifications.

Citations

• Lexsegment ideals are sequentially Cohen-Macaulay
• Stanley conjecture on intersections of four monomial prime ideals

Related

• Depth and minimal number of generators of square free monomial ideals
• Depth of some special monomial ideals
• Depth of some square free monomial ideals
• Depth in a pathological case
• Stanley depth on five generated, squarefree, monomial ideals