Abstract
We use matrix wreath products to show that (1) every countable dimensional nonsingular algebra is embeddable in a finitely generated nonsingular algebra, (2) for every infinite dimensional finitely generated PI-algebra [Formula: see text] there exists an epimorphism [Formula: see text], where [Formula: see text] and the algebra [Formula: see text] is not representable by matrices over a commutative algebra. If the algebra [Formula: see text] is commutative, then [Formula: see text] satisfies the ACC on two-sided ideals as in the recent examples of Greenfeld and Rowen.
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