Sequentially Cohen-Macaulay monomial ideals of embedding dimension four

2007/02/20 by Sarfraz Ahmad, Ahmad, Sarfraz, Dorin Popescu +1 · 1 citation
Computer Science · Mathematics · #13C14 #13F20 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 13H10 Secondary 13P10

paper · pdf · doi:10.48550/arxiv.math/0702569

openalex publication_date 2007/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I be a monomial ideal of the polynomial ring S=K[x₁,...,x₄] over a field K. Then S/I is sequentially Cohen-Macaulay if and only if S/I is pretty clean. In particular, if S/I is sequentially Cohen-Macaulay then I is a Stanley ideal.

Citations

• Criterions for Shellable Multicomplexes
• Stanley decompositions and partitionable simplicial complexes

Cited by

• Stanley decompositions of squarefree modules and Alexander duality

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