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Advanced Modern Algebra

Advanced Modern Algebra - 02 edition

ISBN13: 978-0130878687

ISBN13: 978-0130878687
ISBN10: 0130878685
Cover type:
Edition/Copyright: 02
Publisher: Prentice Hall, Inc.
Published: 2002
International: No

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Advanced Modern Algebra - 02 edition

ISBN13: 978-0130878687

Joseph J. Rotman

ISBN13: 978-0130878687
ISBN10: 0130878685
Cover type:
Edition/Copyright: 02
Publisher: Prentice Hall, Inc.

Published: 2002
International: No

Author Bio

Rotman, Joseph J. : University of Illinois, Urbana-Champaign

Table of Contents

Preface.
Special Notation.


1. Things Past.
Some Number Theory. Roots of Unity. Some Set Theory.

2. Groups I.
Introduction. Permutations. Groups. Lagrange's Theorem. Homomorphisms. Quotient Groups. Group Actions.

3. Commutative Rings I.
Introduction. First Properties. Polynomials. Greatest Common Divisors. Homomorphisms. Euclidean Rings. Linear Algebra. Quotient Rings and Finite Fields. Epilog.

4. Fields.
Introduction. Insolvability of the Quintic. Fundamental Theorem of Galois Theory.

5. Groups II.
Finite Abelian Groups. The Sylow Theorems. The Jordan-Hölder Theorem. PSL (2,k). Presentations. The Neilsen-Schreier Theorem.

6. Commutative Rings II.
Prime Ideals and Maximal Ideals. Unique Factorization Domains. Noetherian Rings. Applications of Zorn's Lemma. Varieties. Gröbner Bases.

7. Modules and Categories.
Modules. Categories. Functors. Free Modules, Projectives, and Injectives. Limits.

8. Algebras.
Noncommutative Rings. The Jacobson Radical. Semisimple Rings. Tensor Products. Representations and Burnside's Theorem.

9. Advanced Linear Algebra.
Modules over PIDs. Rational Canonical Forms. Jordan Canonical Forms. Smith Normal Forms. Bilinear Forms. Graded Algebras. Exterior Algebra. Determinants. Lie Algebras.

10. Homology.
Introduction. Semidirect Products. General Extensions and Cohomology. Homology Functors. Ext and Tor. Cohomology of Groups. Epilog.

11. Commutative Rings III.
Dedekind Rings. Global Dimension. Local Rings. Regular Local Rings.

Appendix A: The Axiom of Choice and Zorn's Lemma.
Bibliography.
Index.

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