Computational Aspects of Polynomial Identities

by Alexei Kanel-Belov, Louis Halle Rowen

Overview

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.

Product Details

ISBN-13:	9781568811635
Publisher:	Taylor & Francis
Publication date:	02/22/2005
Series:	Research Notes in Mathematics Series , #9
Pages:	400
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Kanel-Belov, Alexei; Rowen, Louis Halle

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

What People are Saying About This

From the Publisher

" "The present book is written by two of the leading experts in the thoery of PI-algebras and fills a serious gap... It not only contains a comprehensive study of the main research done in polynomial identitites over the last 25 years. Its purpose is also to make more transparent important and difficult topics. I believe that the algebraic community will find the book interesting and useful. The text is suitable both for beginners and experts. The book (or parts of it) may serve as a graduate course on PI-algebras and on combinatorial ring theory. It can be used as a good source of references." -Vesselin Drensky, Mathematiacl Reviews 2006b, February 2006

"As a summary, the book contains a wealth of contemporary material about polynomial identities in associative algebras. It can be recommended to an advanced reader with substantial experience in the theory of PI-algebras." -CMS Reviews, November 2006

"All topics of the monograph are well-arranged and developed in a clear way... suitable not only as a useful reference for researchers but also as part of a course on PI-algebras for graduate students." -EMS, December 2006

"This book, written by masters in this area, beautifully describe [approaches to polynomial identities], partly following the historic development of some famous problems." -Internationale Mathematische Nachrichten, August 2008"

Editorial Reviews

" "The present book is written by two of the leading experts in the thoery of PI-algebras and fills a serious gap... It not only contains a comprehensive study of the main research done in polynomial identitites over the last 25 years. Its purpose is also to make more transparent important and difficult topics. I believe that the algebraic community will find the book interesting and useful. The text is suitable both for beginners and experts. The book (or parts of it) may serve as a graduate course on PI-algebras and on combinatorial ring theory. It can be used as a good source of references." -Vesselin Drensky, Mathematiacl Reviews 2006b, February 2006

"As a summary, the book contains a wealth of contemporary material about polynomial identities in associative algebras. It can be recommended to an advanced reader with substantial experience in the theory of PI-algebras." -CMS Reviews, November 2006

"All topics of the monograph are well-arranged and developed in a clear way... suitable not only as a useful reference for researchers but also as part of a course on PI-algebras for graduate students." -EMS, December 2006

"This book, written by masters in this area, beautifully describe [approaches to polynomial identities], partly following the historic development of some famous problems." -Internationale Mathematische Nachrichten, August 2008"

From the Publisher