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Fundamentals of abstract algebra

This new addition to the International Series in Pure and Applied Mathematics is for the two-term advanced undergraduate course in abstract algebra. Each chapter consists of definitions, theorems, proofs, and corollaries. There are also numerous examples that help illustrate the concepts. A unique f...

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Bibliographic Details
Main Author: Malik, D.S
Other Authors: Mordeson, John N., Sen, M.K
Format: Book
Language:English
Published: New York McGraw-Hill 1997
Series:International series in pure and applied mathematics
Subjects:
Algebra, Abstract
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Table of Contents:
  • 1. Sets, Relations, and Integers
  • 2. Introduction to Groups
  • 3. Permutation Groups
  • 4. Subgroups and Normal Subgroups
  • 5. Homomorphisms and Isomorphisms of Groups
  • 6. Direct Product of Groups
  • 7. Sylow Theorems
  • 8. Solvable and Nilpotent Groups
  • 9. Finitely Generated Abelian Groups
  • 10. Introduction to Rings
  • 11. Subrings, Ideals, and Homomorphisms
  • 12. Ring Embeddings
  • 13. Direct Sum of Rings
  • 14. Polynomial Rings
  • 15. Euclidean Domains
  • 16. Unique Factorization Domains
  • 17. Maximal, Prime, and Primary Ideals
  • 18. Noetherian and Artinian Rings
  • 19. Modules and Vector Spaces
  • 20. Rings of Matrices
  • 21. Field Extensions
  • 22. Multiplicity of Roots
  • 23. Finite Fields
  • 24. Galois Theory and Applications
  • 25. Geometric Constructions
  • 26. Coding Theory
  • 27. Grobner Bases.

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