Computational Aspects of Polynomial Identities: Volume L, Kemer's Theorems, 2nd Edition

ISBN-13: 9780367445805 / Angielski / Miękka / 2019 / 418 str.

Alexei Kanel-Belov; Yakov Karasik; Louis Halle Rowen

Opis

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

Spis treści

Basic Associative PI-Theory: Basic Results. A Few Words Concerning Affine PI-Algebras: Shirshov’s Theorem. Representations of S_n 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.

O autorze

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.