Computational Aspects of Polynomial Identities
Seiten
2019
CRC Press (Verlag)
978-0-367-44650-5 (ISBN)
CRC Press (Verlag)
978-0-367-44650-5 (ISBN)
This book introduces polynomial identity (PI)-algebras and reviews some well-known results and techniques, most of which are associated with the structure theory. It presents a full proof of Kemer's solution to Specht's conjecture.
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.
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.
Kanel-Belov, Alexei; Rowen, Louis Halle
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
| Erscheinungsdatum | 03.12.2019 |
|---|---|
| Verlagsort | London |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 453 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-367-44650-2 / 0367446502 |
| ISBN-13 | 978-0-367-44650-5 / 9780367446505 |
| Zustand | Neuware |
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