Arithmetical rank of binomial ideals

TL;DR

This paper studies the arithmetical rank of binomial ideals, especially binomial edge ideals of graphs, providing bounds and exact values in various cases to deepen understanding of their algebraic properties.

Contribution

It offers new bounds and exact computations for the arithmetical rank of binomial ideals, with a focus on binomial edge ideals of graphs, advancing algebraic understanding.

Findings

Lower bounds for binomial arithmetical rank established

Exact arithmetical rank computed for specific binomial edge ideals

Enhanced understanding of algebraic properties of binomial ideals

Abstract

In this paper, we investigate the arithmetical rank of a binomial ideal $J$. We provide lower bounds for the binomial arithmetical rank and the $J$-complete arithmetical rank of $J$. Special attention is paid to the case where $J$ is the binomial edge ideal of a graph. We compute the arithmetical rank of such an ideal in various cases.