FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 4, PAGES 1193-1203

On decidability of the equational theories of ring varieties of finite characteristic

V. Yu. Popov

Abstract

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It is proved that for every natural number $n>1$ there exists a finitely based variety $\mathfrak X_n$ of (not necessarily associative) rings such that $\mathfrak X_n \models nx=0$, $\mathfrak X_n \not\models mx=0$ for every natural number $m<n$, and the equational theory $\mathfrak X_n$ is undecidable.

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