Equations in Algebras

Olga Kharlampovich, Alexei Myasnikov

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)1517-1533
Number of pages17
JournalInternational Journal of Algebra and Computation
Volume28
Issue number8
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Diophantine problem
  • associative algebra
  • equation
  • group algebra

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