Criteria for the presence of the maximal ideal in the set of associated primes

Abstract

In this paper, we establish some criteria to detect the presence of the maximal ideal $(x_1,\dots ,x_n)$ in the set of associated primes of powers of monomial ideals in the polynomial ring $K[x_1,\dots ,x_n]$. Furthermore, for each of these criteria, we illustrate its applicability with corresponding examples.

This paper is to appear in Contemporary Mathematics, American Mathematical Society (AMS)