Computational Aspects of Polynomial Identities 1st edition By Alexei Kanel Belov, Louis Halle Rowen ISBN 0367446505 9780367446505
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ISBN 10: 0367446505
ISBN 13: 9780367446505
Author: Alexei Kanel Belov, Louis Halle Rowen
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.
Computational Aspects of Polynomial Identities 1st Table of contents:
Chapter 1: Basic Results
Chapter 2: A Few Words Concerning Affine PI-Algebras
Chapter 3: T-Ideals and Relatively Free Algebras
Chapter 4: Specht’s Problem in the Affine Case
Chapter 5: Representations of Sn and Their Applications
Chapter 6: Superidentities and Kemer’s Main Theorem
Chapter 7: PI-Algebras in Characteristic p
Chapter 8: Recent Structural Results
Chapter 9: Poincare-Hilbert Series and Gelfand-Kirillov Dimension
Chapter 10: More Representation Theory
Chapter 11: Unified Theory of Identities
Chapter 12: Trace Identities
Chapter 13: Exercises
Chapter 14: Lists of Theorems and Examples
Chapter 15: Some Open Questions
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Tags: Alexei Kanel Belov, Louis Halle Rowen, Computational Aspects, Polynomial Identities