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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