Robinson-Amitsur ultrafilters, Jonsson lemma, varieties of algebras, and Tarski's monsters

We present a simple yet powerful result about embedding of algebraic systems, which, from one side, generalizes an old ultraproduct construction due to A. Robinson and Amitsur, and, from another side, resembles the celebrated Jonsson lemma from the universal algebra. As an application, we outline alternative proofs of some results from the theory of PI algebras, and establish some properties of Tarski's monsters.