Nikolaus Vonessen, Rings with Polynomial Identities, An Elementary Introduction, Proceedings of the XII Brazilian Algebra Meeting, Matematica Contemporanea 7 (1994), 199-231.

Abstract.

These notes form an elementary introduction to the theory of rings satisfying a polynomial identity.  No background in non-commutative ring theory is assumed; the only prerequisite is familiarity with the fundamental concepts of commutative algebra.