Kanel-Belov, Alexei; Rowen, Louis Halle

" "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"

• 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

Kanel-Belov, Alexei; Rowen, Louis Halle

" "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"

• 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