Steps in Commutative Algebra

ISBN-13: 9780521646239 / Angielski / Miękka / 2001 / 368 str.

R. Y. Sharp; Rodney Y. Sharp; C. M. Series

Opis

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.

Recenzje

'… 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, The Mathematical Gazette

Spis treści

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.