Ascent and descent of the Golod property along algebra retracts

TL;DR

This paper investigates how the Golod property behaves when moving along algebra retracts, providing characterizations and criteria for modules and rings to be Golod, which advances understanding in algebraic structure theory.

Contribution

It introduces new characterizations and criteria for the Golod property in modules and rings, especially in the context of algebra retracts and graded structures.

Findings

Characterization of trivial extensions and fiber products as Golod rings

Criterion for graded modules over affine algebras to be Golod

Insights into ascent and descent of Golod property along algebra retracts

Abstract

We study ascent and descent of the Golod property along an algebra retract. We characterise trivial extensions of modules, fibre products of rings to be Golod rings. We present a criterion for a graded module over a graded affine algebra of characteristic zero to be a Golod module.