A Pi-Algebra which is not Pi when an Inverse is Adjoined
Robert A. Indik · Proceedings of the American Mathematical Society · 1979
An example is produced of an algebra, embedded in $2 \times 2$ matrices over a field, which is not PI when an element’s inverse is formally adjoined. This example is used to show that the generic $2 \times 2$ matrices, a domain, has the same property.