Steps in Commutative Algebra [Paperback]

Introductory account of commutative algebra, aimed at students with a background in basic algebra.This introductory account of commutative algebra is aimed at students with a background only in basic algebra. It is thus suitable for typical mathematics graduate students, but it can also be used for some some final year undergraduate courses. Professor Sharp's intention is to provide 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.This introductory account of commutative algebra is aimed at students with a background only in basic algebra. It is thus suitable for typical mathematics graduate students, but it can also be used for some some final year undergraduate courses. Professor Sharp's intention is to provide 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.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. CohenMacaulay l“8