Computational Aspects of Polynomial Identities

This book introduces polynomial identity (PI)-algebras and reviews some well-known results and techniques, most of which are associated with the structure theory. It presents a full proof of Kemer's solution to Specht's conjecture.

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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.