A comprehensive study of the main research done in polynomial identities over the last 25 years, including Kemer's solution to the Specht problem in characteristic O and examples in the characteristic p situation. The authors also cover codimension theory, starting with Regev's theorem and continuing through the Giambruno-Zaicev exponential rank. The "best" proofs of classical results, such as the existence of central polynomials, the tensor product theorem, the nilpotence of the radical of an affine PI-algebra, Shirshov's theorem, and characterization of group algebras with PI, are presented.
Table of Contents
1. Basic Results 2. Affine Pl-algebras 3. T-ldeals and Relatively Free Algebras 4. Specht's Problem in the Affine Case 5. Representations of Sn and Their Applications 6. Superidentities and Kemer's Main Theorem 7. Pi-Algebras in Characteristic p 8. Recent Structural Results 9. Poincare-Hilbert Series and Gelfand-Kirillov Dimension 10. More Representation Theory 11. Unified Theory of Identities 12. Trace Identities 13. Exercises 14. Lists of Theorems and Examples 15. Some Open Questions
Kanel-Belov, Alexei; Rowen, Louis Halle