On elementary equivalence of rings with a finitely generated additive group

TL;DR

This paper characterizes when two rings with finitely generated additive groups are elementarily equivalent using purely algebraic methods, regardless of other ring properties.

Contribution

It provides a complete algebraic characterization of elementary equivalence for such rings in the language of pure rings, extending understanding in model theory of rings.

Findings

Complete algebraic criteria for elementary equivalence.

Applicable to arbitrary rings with finitely generated additive groups.

Advances the model-theoretic classification of rings.

Abstract

In this paper we provide a complete algebraic characterization of elementary equivalence of rings with a finitely generated additive group in the language of pure rings. The rings considered are arbitrary otherwise.