2016/06/11 by Kharlampovich, Olga, Myasnikov, Alexei
#03C60 #16B70 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1606.03617
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.