FA-presentable groups and rings

DOI10.1016/j.jalgebra.2007.04.015zbMath1165.03017OpenAlexW2041470989MaRDI QIDQ947484

André Nies, Richard M. Thomas

Publication date: 6 October 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.04.015

zbMATH Keywords

Heisenberg groupfirst-order theoryautomatic structuresFA-presentable groupFA-presentable ringfinite-automata-presentable structureslocally finite ringlocally virtually abelian

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Automata and formal grammars in connection with logical questions (03D05) Applications of logic in associative algebras (16B70)

Related Items (15)

UNARY FA-PRESENTABLE SEMIGROUPS ⋮ Finitely Generated Semiautomatic Groups ⋮ Learning pattern languages over groups ⋮ Lamplighter groups and automata ⋮ Word automatic groups of nilpotency class 2 ⋮ Semiautomatic structures ⋮ Finite automata presentable Abelian groups ⋮ Subalgebras of FA-presentable algebras. ⋮ Algebraic structures computable without delay ⋮ Eliminating unbounded search in computable algebra ⋮ The isomorphism problem for tree-automatic ordinals with addition ⋮ The back-and-forth method and computability without delay ⋮ Defining Multiplication in Some Additive Expansions of Polynomial Rings ⋮ Learning Pattern Languages over Groups ⋮ BREAKING UP FINITE AUTOMATA PRESENTABLE TORSION-FREE ABELIAN GROUPS

Uses Software

• AUTOMATA

Cites Work

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• Powers of rationals modulo 1 and rational base number systems
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• Examples of strongly \(\pi\)-regular rings.
• Automatic semigroups
• ON THE ELEMENTARY THEORY OF A FINITELY GENERATED ALMOST SOLVABLE GROUP
• Describing Groups
• Automatic linear orders and trees
• Finite Automata Presentable Abelian Groups
• On a correspondence between rings and groups
• STACS 2005
• Countably compact rings with periodic groups of units

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