English

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.

Keywords

Cite

@article{arxiv.1606.03617,
  title  = {Equations in Algebras},
  author = {Olga Kharlampovich and Alexei Myasnikov},
  journal= {arXiv preprint arXiv:1606.03617},
  year   = {2016}
}
R2 v1 2026-06-22T14:23:12.505Z