A formulation of Euclidean geometry leading to recognition of a new class of algebra isomorphism invariants

Abstract

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

This paper has substantial overlap with arXiv 2306.14995. This is necessary given its unique and fruitful contribution as an alternative derivation of the program of arXiv 2306.14995 via a paradigm arising in Euclidean geometry