Sequentially Cohen-Macaulay and pretty clean monomial ideals

2025/02/27 by Амир Мафи, Mafi, Amir, Rando Rasul Qadir +3
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.2502.20043

openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R=K[x₁,…, x_n] be the polynomial ring in n variables over a field K and I be monomial ideal of R. In this paper, we show that if I is a generic monomial ideal, then R/I is pretty clean if and only if R/I is sequentially Cohen-Macaulay. Furthermore, we prove that this equivalence remains unchanged for some special monomial ideals. Moreover, we provide an example that disproves the conjecture raised in \cite[p. 123]S1 regarding generic monomial ideals.

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