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Abstract Algebra

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Author(s): David M. Burton
Publisher: Wm. C. Brown
Year: 1988

Language: English
Pages: 489+vi
City: Dubuque, Iowa

Title
Contents
Preface
1. Preliminary Notions
1.1. The algebra of sets
1.2. Functions and relations
1.3. Elementary number theory
2. Group Theory
2.1. Arthur Cayley
2.2. Definition and examples of groups
2.3. Certain elementary theorems on groups
2.4. Two important groups
2.5. Subgroups
2.6. Normal subgroups and quotient groups
2.7. Homomorphisms
2.8. The classical isomorphism theorems
3. Further Topics in Group Theory
3.1. Augustin-Louis Cauchy
3.2. Direct products of groups
3.3. The Sylow theorems
3.4. The Jordan-Holder Theorem
4. Ring Theory
4.1. Emmy Noether
4.2. Elementary properties of rings
4.3. Ideals
4.4. Integral domains and fields
4.5. William Rowan Hamilton
4.6. Certain special ideals
4.7. Divisibility theory in integral domains
4.8. Polynomial rings
5. Field Theory
5.1. Evariste Galois
5.2. Vector spaces, bases, and dimension
5.3. Extensions of fields
5.4. The Galois theory of fields
5.5. Equations solvable by radicals
Appendix: Zorn's Lemma
Selected References
Index of Terms
Index of Mathematicians