Promiscuously Quadratic Rings

TL;DR

This paper introduces a new category of quadratic multirings that simplifies functorial relations with quadratic form theories, combining advantages of Special Groups and Realsemigroups while avoiding their drawbacks.

Contribution

It proposes a novel category of quadratic multirings that enhances the theoretical framework for quadratic forms and related algebraic structures.

Findings

Establishes functorial relations with quadratic form theories

Shares properties with Special Groups and Realsemigroups

Avoids drawbacks of existing theories

Abstract

We consider a convenient category of "quadratic" multirings, that allows simple functorial relations with categories associated with abstract quadratic forms theories and shares many good aspects of the theories of Special Groups and of Realsemigroups, but tries to avoids its drawbacks.