# On monomial Golod ideals

## TL;DR

This paper characterizes when monomial ideals in polynomial rings are Golod, providing a complete criterion in three-variable cases and showing that the product of two monomial ideals is Golod.

## Contribution

It offers a complete characterization of Golod monomial ideals in three-variable polynomial rings and proves that their products are Golod.

## Key findings

- Complete characterization of Golod monomial ideals in three variables
- Product of two monomial ideals in three variables is Golod
- Provides ideal-theoretic conditions for Golodness

## Abstract

We study ideal-theoretic conditions for a monomial ideal to be Golod. For ideals in a polynomial ring in three variables, our criteria give a complete characterization. Over such rings, we show that the product of two monomial ideals is Golod.