Lexsegment ideals are sequentially Cohen-Macaulay

2010/10/27 by Muhammad Ishaq, Ishaq, Muhammad · 2 citations
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13H10 #Secondary 13C15

paper · pdf · doi:10.48550/arxiv.1010.5615

openalex publication_date 2010/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The associated primes of an arbitrary lexsegment ideal I⊂ S=K[x₁,...,x_n] are determined. As application it is shown that S/I is a pretty clean module, therefore, S/I is sequentially Cohen-Macaulay and satisfies Stanley's conjecture.

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• Monomial ideals of minimal depth and trivial modifications
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• Sequentially Cohen-Macaulay monomial ideals of embedding dimension four
• Classes of sequentially Cohen-Macaulay squarefree monomial ideals
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