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.
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
'... 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
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