LSC A Book of Abstract Algebra

by Pinter, Charles

• ISBN13: 9780072943504
• ISBN10: 0072943505
• Edition: 2nd
• Format: Paperback
• Copyright: 2003-05-06
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

Accessible but rigorous, this outstanding text encompasses all of elementary abstract algebra's standard topics. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. 1990 edition.

Table of Contents

1. Why Abstract Algebra?

2. Operations

3. The Definition of Groups

4. Elementary Properties of Groups

5. Subgroups

6. Functions

7. Groups of Permutations

8. Permutations of a Finite Set

9. Isomorphism

10. Order of Group Elements

11. Cyclic Groups

12. Partitions and Equivalence Relations

13. Counting Cosets

14. Homomorphisms

15. Quotient Groups

16. The Fundamental Homomorphism Theorem

17. Rings: Definitions and Elementary Properties

18. Ideals and Homomorphisms

19. Quotient Rings

20. Integral Domains

21. The Integers

22. Factoring into Primes

23. Elements of Number Theory (Optional)

24. Rings of Polynomials

25. Factoring Polynomials

26. Substitution in Polynomials

27. Extensions of Fields

28. Vector Spaces

29. Degrees of Field Extensions

30. Ruler and Compass

31. Galois Theory: Preamble

32. Galois Theory: The Heart of the Matter

33. Solving Equations by Radicals

Appendix A: Review of Set Theory

Appendix B: Review of the Integers

Appendix C. Review of Mathematical Induction

Answers Selected Exercises

Index