Let I be a square-free monomial ideal in a polynomial ring R= K [x 1,…, xn] over a field K,
𝔪=(x 1,…, xn) be the graded maximal ideal of R, and {u 1,…, u β 1 (I)} be a maximal …

An ideal I in a commutative Noetherian ring R has the strong persistence property if (I t+ 1:
RI)= I t for all positive integers t. In this article, we focus on how some graph operations affect …

Let R be a commutative Noetherian ring and I be an ideal of R. Then, I has the strong
persistence property if (Ik+ 1: RI)= Ik for all k. Also, we say that I has the symbolic strong …

Abstract The sequence (Ass (R/I n)) n∈ N of associated primes of powers of a monomial
ideal I in a polynomial ring R eventually stabilizes by a known result by Markus Brodmann …

The main aim of this work is to study several topics in monomial ideals. Generally, monomial
ideals play a fundamental role in investigating the connection between commutative algebra …

Let R be a commutative Noetherian ring and I be an ideal of R. We say that I satisfies the
persistence property if AssR (R/Ik)⊆ AssR (R/Ik+ 1) for all positive integers k, where AssR …