UNDECIDABILITY OF EQUATIONS IN FREE LIE ALGEBRAS

被引：2

作者：

Kharlampovich, Olga ^{[1
]}

Myasnikov, Alexei ^{[2
]}

机构：

[1] CUNY Hunter Coll, Dept Math & Stat, New York, NY 10065 USA

[2] Stevens Inst Technol, Dept Math Sci, Hoboken, NJ 07030 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 371卷 / 04期

关键词：

DIOPHANTINE PROBLEM; ELEMENTARY THEORY;

D O I：

10.1090/tran/7579

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least 3 with coefficients in an arbitrary integral domain. We also show that the ring of integers Z is interpretable by positive existential formulas in such free Lie algebras if the integral domain has characteristic 0.

引用

页码：2987 / 2999

页数：13

共 26 条

[1]

[Anonymous], 1970, DOKL AKAD NAUK SSSR+

[2]

Bahturin Yu. A., 1987, IDENTICAL RELATIONS

[3] On Systems of Equations over Free Partially Commutative Groups [J].

Casals-Ruiz, Montserrat ;

Kazachkov, Ilya .

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 212 (999) :1-+

[4] On systems of equations over free products of groups [J].

Casals-Ruiz, Montserrat ;

Kazachkov, Ilya V. .

JOURNAL OF ALGEBRA, 2011, 333 (01) :368-426

[5] The isomorphism problem for toral relatively hyperbolic groups [J].

Dahmani, Francois ;

Groves, Daniel .

PUBLICATIONS MATHEMATIQUES, NO 107, 2008, 107 (107) :211-+

[6] Bounded algebraic geometry over a free lie algebra [J].

Daniyarova E.Y. ;

Remeslennikov V.N. .

Algebra and Logic, 2005, 44 (3) :148-167

[7] Algebraic geometry over free metabelian lie algebras. II. Finite-field case [J].

Daniyarova E.Yu. ;

Kazatchkov I.V. ;

Remeslennikov V.N. .

Journal of Mathematical Sciences, 2006, 135 (5) :3311-3326

[8]

Daniyarova E.Yu., 2003, FUNDAM PRIKL MAT, V9, P37

[9] DIOPHANTINE PROBLEM FOR POLYNOMIAL RINGS AND FIELDS OF RATIONAL FUNCTIONS [J].

DENEF, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 242 (AUG) :391-399

[10]

Denef J., 1979, Logic Colloquium 78, P131

← 1 2 3 →