Arithmetical rank of Cohen-Macaulay squarefree monomial ideals of height two

TL;DR

This paper proves that squarefree monomial ideals of height two with Cohen-Macaulay quotient rings are set-theoretic complete intersections, advancing understanding of their algebraic structure.

Contribution

It establishes that such ideals are set-theoretic complete intersections, a new result linking Cohen-Macaulay property and ideal structure.

Findings

Squarefree monomial ideals of height 2 are set-theoretic complete intersections.

Cohen-Macaulay quotient rings imply the ideal is a set-theoretic complete intersection.

Provides a characterization of these ideals in algebraic geometry and commutative algebra.

Abstract

In this paper, we prove that a squarefree monomial ideal of height 2 whose quotient ring is Cohen-Macaulay is set-theoretic complete intersection.