UID:
almahu_9947367181502882
Format:
1 online resource (387 p.)
ISBN:
1-281-76894-4
,
9786611768942
,
0-08-087400-2
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; 84
Content:
Polynomial identities in ring theory
Note:
Description based upon print version of record.
,
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
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1.10. Valuation Rings, Idempotent Lifting, and Their Applications1.11. 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
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3.3. The Generic Division RingsExercises; 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
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6.1. The Solution of the Tensor Product Question6.2. 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
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8.1. Definitions and Examples8.2. 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
,
English
Additional Edition:
ISBN 0-12-599850-3
Language:
English
