Commutative Algebra [Paperback]

This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry.This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.1. Preliminaries; 2. Flatness; 3. Fractions; 4. Supporting and associated prime ideals; 5. Integers; 6. Some geometrical results; 7. Valuation rings; 8. Pr?fer and Dedekind rings; 9. General exercises; Appendices; Bibliography; Indices.