Equations in Algebras
Logic
2016-06-28 v2
Abstract
We show that the Diophantine problem(decidability of equations) is undecidable in free associative algebras over any field and in the group algebras over any field of a wide variety of torsion free groups, including toral relatively hyperbolic groups, right angled Artin groups, commutative transitive groups, the fundamental groups of various graph groups, etc.
Cite
@article{arxiv.1606.03617,
title = {Equations in Algebras},
author = {Olga Kharlampovich and Alexei Myasnikov},
journal= {arXiv preprint arXiv:1606.03617},
year = {2016}
}