Fundamentals of abstract algebra

By: Malik, D.SContributor(s): Mordeson, John M | Sen, M.KMaterial type: TextTextSeries: International series in pure and applied mathematicsPublication details: New York : McGraw-Hill, ©1997Description: xix, 636 pages : illustrationsISBN: 9780070400351; 0070400350 ; 9780071154222 ; 71154221 Subject(s): Algebra, AbstractDDC classification: 512.02
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.
Summary: 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 feature of this text is the worked-out exercises that appear after every section. These worked-out exercises provide techniques of problem solving for students. Sprinkled throughout the text are comments dealing with the historical development of abstract algebra as well as profiles of notable mathematicians. Special topics, such as algebraic varieties, matrix rings, and Noetherian and Artinian rings, are also included for those instructors who want additional material.
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Includes Bibliography & Index

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.


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 feature of this text is the worked-out exercises that appear after every section. These worked-out exercises provide techniques of problem solving for students. Sprinkled throughout the text are comments dealing with the historical development of abstract algebra as well as profiles of notable mathematicians. Special topics, such as algebraic varieties, matrix rings, and Noetherian and Artinian rings, are also included for those instructors who want additional material.

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