Baer orderings and involutive multialgebras - Santos, Kaique Ribeiro Prates (2026)
The aim of this work is to advance the study of a new frontier: the theory of involutive multialgebras and their orderings. We pursue two main lines of investigation: the application of matroid theory as a tool to describe the structure of Baer ordering spaces, and the characterization of a class of involutive multirings that extends the notion of reduced real multirings, namely, the reduced convex multirings. The necessary tools are developed through Marshalls quotients and prototypical examples, while relying on classical results concerning involutive algebras, Baer (weak) orderings, and the characterization of the combinatorial geometries that describe ordering spaces.