Elementary equivalence of rings with finitely generated additive groups

Elementary equivalence of rings with finitely generated additive groups

We give algebraic characterizations of elementary equivalence between rings with finitely generated additive groups. They are similar to those previously obtained for finitely generated nilpotent groups. Here, the rings are not supposed associative, commutative or unitary.

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Veröffentlicht in:Annals of pure and applied logic 2018-06, Vol.169 (6), p.514-522
Hauptverfasser: Myasnikov, Alexei G., Oger, Francis, Sohrabi, Mahmood
Format: Artikel
Sprache:eng
Schlagworte:
Bilinear map
Definable scalar ring
Elementary equivalence
Group Theory
Logic
Mathematics
Nilpotent group
Ring
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Zusammenfassung:We give algebraic characterizations of elementary equivalence between rings with finitely generated additive groups. They are similar to those previously obtained for finitely generated nilpotent groups. Here, the rings are not supposed associative, commutative or unitary.
ISSN:0168-0072
DOI:10.1016/j.apal.2018.01.005