Résumé
This introductory account of commutative algebra is aimed
at advanced undergraduates and first year graduate
students. Assuming only basic abstract algebra, it provides
a good foundation in commutative ring theory, from which
the reader can proceed to more advanced works in
commutative algebra and algebraic geometry. The style
throughout is rigorous but concrete, with exercises and
examples given within chapters, and hints provided for the
more challenging problems used in the subsequent
development. After reminders about basic material on
commutative rings, ideals and modules are extensively
discussed, with applications including to canonical forms
for square matrices. The core of the book discusses the
fundamental theory of commutative Noetherian rings. Affine
algebras over fields, dimension theory and regular local
rings are also treated, and for this second edition two
further chapters, on regular sequences and
Cohen–Macaulay rings, have been added. This book is
ideal as a route into commutative algebra.
Contents
- Prefaces to the 1st and 2nd editions
- 1. Commutative rings and subrings
- 2. Ideals
- 3. Prime ideals and maximal ideals
- 4. Primary decomposition
- 5. Rings of fractions
- 6. Modules
- 7. Chain conditions on modules
- 8. Commutative Noetherian rings
- 9. More module theory
- 10. Modules over principal ideal domains
- 11. Canonical forms for square matrices
- 12. Some applications to field theory
- 13. Integral dependence on subrings
- 14. Affine algebras over fields
- 15. Dimension theory
- 16. Regular sequences and grade
- 17. Cohen–Macaulay rings
- Bibliography
- Index.
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Cambridge University Press |
| Auteur(s) | R. Y. Sharp |
| Parution | 16/10/2001 |
| Nb. de pages | 354 |
| Format | 15 x 22,8 |
| Couverture | Broché |
| Poids | 495g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780521646239 |
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