# Non Reduced Theory of Quadratic Forms Over Rings

## TL;DR

This paper develops a non-reduced abstract quadratic forms theory over rings using multirings and multifields, expanding the foundational understanding of quadratic forms beyond traditional reduced frameworks.

## Contribution

It introduces a novel non-reduced quadratic forms framework over rings, leveraging multiring and multifield structures, which broadens the theoretical landscape.

## Key findings

- Establishment of a non-reduced quadratic forms theory
- Application of multiring and multifield machinery
- Extension of quadratic forms theory to general coefficients

## Abstract

Based on the works of M. Marshall on multirings, we propose the fundamentals for a \textbf{non reduced} abstract quadratic forms theory in general coefficients on rings, with the machinery of multirings and multifields.