# Some criteria for detecting large homomorphisms of local rings

## TL;DR

This paper investigates ideals in local rings that produce large homomorphisms upon quotienting, providing characterizations over specific classes like complete intersections, Koszul, and Golod rings.

## Contribution

It offers new characterizations of ideals inducing large homomorphisms in various classes of local rings, expanding understanding of their structural properties.

## Key findings

- Characterization over complete intersections
- Characterization over Koszul rings
- Characterization over Golod rings

## Abstract

We study ideals in a local ring $R$ whose quotient rings induce large homomorphisms of local rings. We characterize such ideals over complete intersections, Koszul rings, and over some classes of Golod rings.