Equations in Algebras

Olga Kharlampovich; Alexei Myasnikov

doi:10.1142/S0218196718400064

Equations in Algebras

Olga Kharlampovich
, Alexei Myasnikov

Department of Mathematical Sciences

City University of New York

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1517-1533
Number of pages	17
Journal	International Journal of Algebra and Computation
Volume	28
Issue number	8
DOIs	https://doi.org/10.1142/S0218196718400064
State	Published - 1 Dec 2018

Keywords

Diophantine problem
associative algebra
equation
group algebra

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10.1142/S0218196718400064

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title = "Equations in Algebras",

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.",

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AU - Myasnikov, Alexei

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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

UR - https://www.scopus.com/pages/publications/85044557098

UR - https://www.scopus.com/pages/publications/85044557098#tab=citedBy

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DO - 10.1142/S0218196718400064

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VL - 28

SP - 1517

EP - 1533

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 8

ER -

Equations in Algebras

Abstract

Keywords

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