Polynomial Identities in Ring Theory
Published on 24. July 1980
365 pages
978-0-08-087400-5 (ISBN)
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Polynomial Identities in Ring Theory
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Louis Halle Rowen
Polynomial Identities in Ring Theory
Book
01/1980
Academic Press
€100.90
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Content
- Front Cover
- Polynomial Identities in Ring Theory
- Copyright Page
- Contents
- Preface
- Prerequisites
- Chapter 1. The Structure of PI-Rings
- 1.1. Basic Concepts and Examples
- 1.2. Facts about Normal Polynomials
- 1.3. Matrix Algebras
- 1.4. Identities and Central Polynomials for Matrix Algebras, and Their Applications to Arbitrary Pl-Algebras
- 1.5. Primitive Rings, Kaplansky's Theorem, and Semiprimitive Rings
- 1.6. Injections of Algebras, Featuring Various Nil Radicals
- 1.7. Central Localization of PI-Algebras
- 1.8. Tensor Products and the Artin-Procesi Theorem
- 1.9. The Prime Spectrum
- 1.10. Valuation Rings, Idempotent Lifting, and Their Applications
- 1.11. Identities of Rings without 1
- Exercises
- Chapter 2. The General Theory of Identities, and Related Theories
- 2.1. Basic Concepts
- 2.2. PI-Rings Which Have an Involution
- 2.3. Sets of Identities of Related Rings (with Involution)
- 2.4. Relatively Free PI-Rings and T-Ideals
- 2.5. Identities of Matrix Rings with Involution
- 2.6. Elementary Sentences of Algebraic Systems
- Exercises
- Chapter 3. Central Simple Algebras
- 3.1. Fundamental Results
- 3.2. Positive General Results about Maximal Subfields of Division Rings
- 3.3. The Generic Division Rings
- Exercises
- Chapter 4. Extensions of PI-Rings
- 4.1. Integral and Algebraic Extensions of PI-Rings
- 4.2. Formal Words and Shirshov's Solution to the Kurosch Problem
- 4.3. The Characteristic Closure of a Prime PI-Ring
- 4.4. Finitely Generated PI-Extensions
- 4.5. Generalizing the Razmyslov-Schelter Construction
- Exercises
- Chapter 5. Noetherian PI-Rings
- 5.1. Sufficient Conditions for a PI-Ring to Be Noetherian
- 5.2. The Theory of Noetherian PI-Rings
- Exercises
- Chapter 6. The Theory of the Free Ring, Applied to Polynomial Identities
- 6.1. The Solution of the Tensor Product Question
- 6.2. Representations of Sym(n)
- 6.3. Finite Generation of Certain T-Ideals
- Exercises
- Chapter 7. The Theory of Generalized Identities
- 7.1. Semiprime Rings with Socle
- 7.2. The Basic Theorem of Generalized Polynomials and Its Consequences
- 7.3. Primitive Rings with Involution
- 7.4. Identities and Generalized Identities of Rings with Involution
- 7.5. Ultraproducts and Their Application to GI-Theory
- 7.6. Martindale's Central Closure
- Exercises
- Chapter 8. Rational Identities, Generalized Rational Identities, and Their Applications
- 8.1. Definitions and Examples
- 8.2. Generalized Rational Identities of Division Rings
- 8.3. Rational Identities of Division Rings of Finite Degree
- 8.4. Applications of the Theory of Rational Identities
- Appendix A: Central Polynomials of Formanek
- Exercises
- Appendix B: The Theory of AE Elementary Conditions on Rings
- Exercises
- Appendix C: Nonassociative PI-Theory
- Exercises
- Postscript: Some Aspects of the History
- Bibliography
- Major Theorems Concerning Identities
- Major Counterexamples
- List of Principal notation
- Index
- Pure and Applied Mathematics
