Alexei Kanel-Belov, Yakov Karasik, Louis Halle Rowen

Computational Aspects of Polynomial Identities (eBook, PDF)

Volume l, Kemer's Theorems, 2nd Edition

• Format: PDF

Produktbeschreibung

This edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. It gives all the details involved in Kemer's proof of Specht's conjecture for affine PI-algebras in characteristic 0. This edition presents a tighter formulation of Zubrilin's theory and contains a more direct proof of the Wehrfritz-Beidar theorem. It also adds more details to the proof of Kemer's difficult PI-representability theorem and develops several newer techniques, such as the "pumping procedure."

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 444
• Erscheinungstermin: 22. Oktober 2015
• Englisch
• ISBN-13: 9781498720090
• Artikelnr.: 44199212

Autorenporträt

Alexei Kanel-Belov is a professor in the Department of Mathematics at Bar-Ilan University. His research interests include ring theory, semigroup theory, polynomial automorphisms, quantization, symbolical dynamic combinatorial geometry and its mechanical applications, elementary mathematics, and mathematical education.

Yakov Karasik completed his doctorate at the Department of Mathematics at Technion - Israel Institute of Technology.

Louis Halle Rowen is a professor in the Department of Mathematics at Bar-Ilan University. His research interests include noncommutative algebra, finite dimensional division algebras, the structure theory of rings, and tropical algebras.

Inhaltsangabe

Basic Associative PI
Theory: Basic Results. A Few Words Concerning Affine PI
Algebras: Shirshov's Theorem. Representations of Sn and Their Applications. Affine PI
Algebras: The Braun
Kemer
Razmyslov Theorem. Kemer's Capelli Theorem. Specht's Conjecture: Specht's Problem and Its Solution in the Affine Case (Characteristic 0). Superidentities and Kemer's Solution for Non
Affine Algebras. Trace Identities. PI
Counterexamples in Characteristic p. Other Results for Associative PI
Algebras: Recent Structural Results. Poincaré
Hilbert Series and Gelfand
Kirillov Dimension. More Representation Theory. Supplementary Material: List of Theorems. Some Open Questions. Bibliography.