Powers are Golod

TL;DR

This paper proves that for a proper graded ideal in a positively graded polynomial ring over a field of characteristic zero, the quotient ring by any power of the ideal (k ≥ 2) is Golod, revealing a broad class of Golod rings.

Contribution

It establishes that all powers (k ≥ 2) of a proper graded ideal in such polynomial rings are Golod, extending the understanding of Golod properties in algebra.

Findings

All powers of the ideal are Golod for k ≥ 2.

The result applies to polynomial rings over fields of characteristic zero.

Provides new insights into the structure of quotient rings by ideal powers.

Abstract

Let $I$ be a proper graded ideal in a positively graded polynomial ring $S$ over a field of characteristic 0. In this note it is shown that $S/I^k$ is Golod for all $k\geq 2$.