chapter  6
46 Pages

Specht’s Problem and Its Solution in the Affine Case (Characteristic 0)

Exercises for Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

In this part, we turn to Specht’s Problem, perhaps the question most discussed in PI-theory. Its solution remains one of the most difficult in the theory, and also, as we shall see, different versions of the question have varying answers: There is a positive solution for (associative) algebras of characteristic 0, but in positive characteristic the answer is positive only for affine algebras, as shown in Volume II (where various results also are given for nonassociative algebras).