TY - JOUR
T1 - Equations in Algebras
AU - Kharlampovich, Olga
AU - Myasnikov, Alexei
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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.
KW - Diophantine problem
KW - associative algebra
KW - equation
KW - group algebra
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U2 - 10.1142/S0218196718400064
DO - 10.1142/S0218196718400064
M3 - Article
AN - SCOPUS:85044557098
SN - 0218-1967
VL - 28
SP - 1517
EP - 1533
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
IS - 8
ER -