This conversational introduction to abstract algebra takes a modern, rings-first approach. In addition to its unconventional order of classical material, another key feature is the treatment of topics often neglected in undergraduate textbooks, such as modules. More than 400 exercises are included, 150 of which are carefully worked out.
This conversational introduction to abstract algebra takes a modern, rings-first approach. In addition to its unconventional order of classical material, another key feature is the treatment of topics often neglected in undergraduate textbooks, such as modules. More than 400 exercises are included, 150 of which are carefully worked out.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Paolo Aluffi is Professor of Mathematics at Florida State University. Aluffi earned a Ph.D. from Brown University with a dissertation on the enumerative geometry of plane cubic curves, under the supervision of William Fulton. His research interests are in algebraic geometry, particularly intersection theory and its application to the theory of singularities and connections with theoretical physics. He has authored about 70 research publications and given lectures on his work in 15 countries. Beside Notes from the Underground, he has published a graduate-level textbook in algebra (Algebra: Chapter 0, AMS) and a mathematics book for the general public, in Italian (Fare matematica, Aracne Editrice).
Inhaltsangabe
Part I. Rings: 1. The integers 2. Modular arithmetic 3. Rings 4. The category of rings 5. Canonical decomposition, quotients, and isomorphism theorems 6. Integral domains 7. Polynomial rings and factorization Part II. Modules: 8. Modules and abelian groups 9. Modules over integral domains 10. Abelian groups Part III. Groups: 11. Groups - preliminaries 12. Basic results on finite groups Part IV. Fields: 13. Field extensions 14. Normal and separable extensions, and splitting fields 15. Galois theory.
Part I. Rings: 1. The integers 2. Modular arithmetic 3. Rings 4. The category of rings 5. Canonical decomposition, quotients, and isomorphism theorems 6. Integral domains 7. Polynomial rings and factorization Part II. Modules: 8. Modules and abelian groups 9. Modules over integral domains 10. Abelian groups Part III. Groups: 11. Groups - preliminaries 12. Basic results on finite groups Part IV. Fields: 13. Field extensions 14. Normal and separable extensions, and splitting fields 15. Galois theory.
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