Steps in Commutative Algebra

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April 2004



This introductory account of commutative algebra is aimed at students with a background only in basic algebra. Professor Sharp's book provides a good foundation from which the reader can proceed to more advanced works in commutative algebra or algebraic geometry. This new edition contains additional chapters on regular sequences and on Cohen-Macaulay rings.


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.


'... a very useful stepping-stone for students in their study of commutative algebra.' H. Mitsch, Wien '... Sharp is an excellent guide, clearly aiming never to leave his readers floundering ... This standard of care for his readers is maintained throughout the book ... this is a superb guide to an attractive and important area of mathematics, and one from which I will derive pleasure as a retirement project. But it will never be an easy ride.' John Baylis, Nottingham Trent University, , The Mathematical Gazette
EAN: 9780521646239
ISBN: 0521646235
Untertitel: 'London Mathematical Society St'. Revised. Sprache: Englisch.
Erscheinungsdatum: April 2004
Seitenanzahl: 368 Seiten
Format: kartoniert
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