Abstract Algebra

Textbook for use by undergraduate mathematics majors. Annotation copyright Book News, Inc. Portland, Or. 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