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 A there exists an epimorphism (A) over cap -> (phi)A, where (ker phi)(3) = (0) and the algebra (A) over cap is not representable by matrices over a commutative algebra. If the algebra A is commutative, then (A) over cap satisfies the ACC on two-sided ideals as in the recent examples of Greenfeld and Rowen.