Algebra: A Graduate Course / Edition 1

Algebra: A Graduate Course / Edition 1

by I. Martin Isaacs
ISBN-10:
0534190022
ISBN-13:
2900534190025
Pub. Date:
11/28/1993
Publisher:
Cengage Learning
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Overview

Algebra: A Graduate Course / Edition 1

From the abstract, axiomatic point of view that prevails today, one can argue that group theory is, in some sense, more primitive than most other parts of algebra and, indeed, the group axioms constitute a subset of the axiom systems that define the other algebraic objects considered in this book. The subject we call 'algebra' was not born abstract. In its youth, algebra was the study of concrete objects such as polynomials, rater than of things defined by axiom systems.

Product Details

ISBN-13: 2900534190025
Publisher: Cengage Learning
Publication date: 11/28/1993
Series: Mathematics Series
Edition description: New Edition
Pages: 528
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

Table of Contents

PART I: NONCOMMUTATIVE ALGEBRA 1. Definitions and Examples of Groups 2. Subgroups and Cosets 3. Homomorphisms 4. Group Actions 5. The Sylow Theorems and p-groups 6. Permutation Groups 7. New Groups from Old 8. Solvable and Nilpotent Groups 9. Transfer 10. Operator Groups and Unique Decompositions 11. Module Theory without Rings 12. Rings, Ideals, and Modules 13. Simple Modules and Primitive Rings 14. Artinian Rings and Projective Models 15. An Introduction to Character Theory PART II: COMMUTATIVE ALGEBRA 16. Polynomial Rings, PIDs, and UFDs 17. Field Extensions 18. Galois Theory 19. Separability and Inseparability 20. Cyclotomy and Geometric Constructions 21. Finite Fields 22. Roots, Radicals, and Real Numbers 23. Norms, Traces, and Discriminants 24. Transcendental Extensions 25. The Artin-Schreier Theorem 26. Ideal Theory 27. Noetherian Rings 28. Integrality 29. Dedekind Domains 30. Algebraic Sets and the Nullstellensatz Index

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