Strong persistence and associated prime of powers of monomial ideals

2022/02/10 by Mafi, Amir, Saremi, Hero
#13C15 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A15 #Secondary 13A30

paper · doi:10.48550/arxiv.2202.05319

Abstract

Let R=K[x₁,…, x_n] be the polynomial ring in n variables over a field K and I be a monomial ideal of degree d≤ 2. We show that (I^k+1:I)=I^k for all k≥ 1 and we disprove a motivation question that was appeared in \cite[Question 2.51]CHHV by providing of a counterexample. Also, by this counterexample, we give a negative answer to the question that depth function of square-free monomial ideals are non-increasing.

Related

• Persistence and stability properties of powers of ideals
• On the Stanley depth of powers of monomial ideals
• An Increasing normalized depth function
• A family of monomial ideals with the persistence property
• Stability of depth and Stanley depth of symbolic powers of squarefree monomial ideals