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Noncommutative algebraic geometry, I: Monomial equations with a single variable

Zlil Sela
Vol. 3 (2024), No. 3, 733–800
DOI: 10.2140/mt.2024.3.733
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 monomial system of equations. Then we analyze the set of solutions to monomial systems of equations with a single variable.

Keywords
varieties, systems of equations, associative algebra, Makanin–Razborov diagram
Mathematical Subject Classification
Primary: 16S10
Secondary: 03C68, 20F65
Milestones
Received: 20 March 2022
Revised: 28 March 2024
Accepted: 8 April 2024
Published: 12 August 2024
Authors
Zlil Sela
Mathematics Department
Hebrew University
Jerusalem
Israel
© 2024 MSP (Mathematical Sciences Publishers).