Abstract
A new family of
finite-dimensional algebras.
This paper defines myrion algebras: finite-dimensional real algebras that extend the complex numbers through an ordered sequence of basis elements. They are unital, commutative, and distributive, while becoming non-associative above two dimensions.
It introduces the singular division locus, which identifies elements whose multiplication operators are singular, and proves that every element has a square root within the same finite-dimensional myrion algebra.