Computational Aspects of Polynomial Identities: Kemer's Theorems: Vol 1
Language: English
Published by Chapman & Hall, 2015
Series: Book 19 of 79 - Chapman & Hall/CRC Monographs and Research Notes in Mathematics
- Hardcover
- New
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2nd edition. 424 pages. 9.53x6.46x1.14 inches. In Stock.
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- Title
- Computational Aspects of Polynomial Identities: Kemer's Theorems: Vol 1
- Author
- Alexey, Belov/ Karasik, Yaakov/ Rowen, Louis Halle
- Publisher
- Chapman & Hall
- Publication year
- 2015
- Condition
- Brand New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 1498720080
- ISBN 13
- 9781498720083
- Edition
- 2nd Edition
- Item weight
- 0.8 kilograms
- Series
- Book 19 of 79: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Computational Aspects of Polynomial Identities: Volume l, Kemer’s Theorems, 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer’s proof of Specht’s conjecture for affine PI-algebras in characteristic 0.
The book first discusses the theory needed for Kemer’s proof, including the featured role of Grassmann algebra and the translation to superalgebras. The authors develop Kemer polynomials for arbitrary varieties as tools for proving diverse theorems. They also lay the groundwork for analogous theorems that have recently been proved for Lie algebras and alternative algebras. They then describe counterexamples to Specht’s conjecture in characteristic p as well as the underlying theory. The book also covers Noetherian PI-algebras, Poincaré–Hilbert series, Gelfand–Kirillov dimension, the combinatoric theory of affine PI-algebras, and homogeneous identities in terms of the representation theory of the general linear group GL.
Through the theory of Kemer polynomials, this edition shows that the techniques of finite dimensional algebras are available for all affine PI-algebras. It also emphasizes the Grassmann algebra as a recurring theme, including in Rosset’s proof of the Amitsur–Levitzki theorem, a simple example of a finitely based T-ideal, the link between algebras and superalgebras, and a test algebra for counterexamples in characteristic p.
"Synopsis" may belong to another edition of this title.
About the Author
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.
"About the title" may belong to another edition of this title.
Revaluation Books
Exeter, United Kingdom
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