# $n$-absorbing monomial ideals in polynomial rings

## TL;DR

This paper investigates the invariant (I) for monomial ideals in polynomial rings, calculating its value for specific cases, thereby enhancing understanding of n-absorbing ideals in algebraic structures.

## Contribution

It provides explicit calculations of (I) for certain monomial ideals in polynomial rings, extending the theory of n-absorbing ideals.

## Key findings

- (I) values are computed for specific monomial ideals
- The work advances understanding of n-absorbing properties in polynomial rings
- Results contribute to the classification of monomial ideals based on (I)

## Abstract

In a commutative ring $R$ with unity, given an ideal $I$ of $R$, Anderson and Badawi in 2011 introduced the invariant $\omega(I)$, which is the minimal integer $n$ for which $I$ is an $n$-absorbing ideal of $R$. In the specific case that $R = k[x_{1}, \ldots, x_{n}]$ is a polynomial ring over a field $k$ in $n$ variables $x_{1},\ldots, x_{n}$, we calculate $\omega(I)$ for certain monomial ideals $I$ of $R$.