Non Commutative Algebraic Geometry I: Monomial Equations with a Single Variable

Abstract

This paper is the first in a sequence on the structure of sets of solutions to systems of equations over a free associative algebra. We start by constructing a Makanin-Razborov diagram that encodes all the homogeneous solutions to a homogeneous system of equations. Then we analyze the set of solutions to monomial systems of equations with a single variable.