Elementary equivalence of rings with finitely generated additive groups

Alexei G. Myasnikov; Francis Oger; Mahmood Sohrabi

doi:10.1016/j.apal.2018.01.005

Elementary equivalence of rings with finitely generated additive groups

Department of Mathematical Sciences

Université Paris Cité

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	514-522
Number of pages	9
Journal	Annals of Pure and Applied Logic
Volume	169
Issue number	6
DOIs	https://doi.org/10.1016/j.apal.2018.01.005
State	Published - Jun 2018

Keywords

Bilinear map
Definable scalar ring
Elementary equivalence
Nilpotent group
Ring

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10.1016/j.apal.2018.01.005

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title = "Elementary equivalence of rings with finitely generated additive groups",

abstract = "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.",

keywords = "Bilinear map, Definable scalar ring, Elementary equivalence, Nilpotent group, Ring",

author = "Myasnikov, \{Alexei G.\} and Francis Oger and Mahmood Sohrabi",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = jun,

doi = "10.1016/j.apal.2018.01.005",

language = "English",

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T1 - Elementary equivalence of rings with finitely generated additive groups

AU - Myasnikov, Alexei G.

AU - Oger, Francis

AU - Sohrabi, Mahmood

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

KW - Bilinear map

KW - Definable scalar ring

KW - Elementary equivalence

KW - Nilpotent group

KW - Ring

UR - https://www.scopus.com/pages/publications/85041129879

UR - https://www.scopus.com/pages/publications/85041129879#tab=citedBy

U2 - 10.1016/j.apal.2018.01.005

DO - 10.1016/j.apal.2018.01.005

M3 - Article

AN - SCOPUS:85041129879

SN - 0168-0072

VL - 169

SP - 514

EP - 522

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 6

ER -

Elementary equivalence of rings with finitely generated additive groups

Abstract

Keywords

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