Elementary equivalence of rings with finitely generated additive groups

DOI10.1016/j.apal.2018.01.005zbMath1505.03083OpenAlexW2963521692MaRDI QIDQ1709681

Francis Oger, Mahmood Sohrabi, Alexei G. Myasnikov

Publication date: 6 April 2018

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2018.01.005

zbMATH Keywords

ringnilpotent groupelementary equivalencebilinear mapdefinable scalar ring

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Structure theory for nonassociative algebras (17A60) Generators, relations, and presentations of groups (20F05) Applications of logic in associative algebras (16B70)

Related Items

First-order rigidity of rings satisfying polynomial identities ⋮ Diophantine problems in solvable groups

Cites Work

• Cancellation and elementary equivalence of groups
• Definable invariants of bilinear mappings
• Separating Classes of Groups by First-Order Sentences
• The Undecidability of Algebraic Rings and Fields
• Cancellation and Elementary Equivalence of Finitely Generated Finite-By-Nilpotent Groups
• THE STRUCTURE OF MODELS AND A DECIDABILITY CRITERION FOR COMPLETE THEORIES OF FINITE-DIMENSIONAL ALGEBRAS
• Quasi-finitely axiomatizable nilpotent groups
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