Commutative algebra with a view toward algebraic geometry / David Eisenbud

Includes bibliographical references (pages 757-774) and indexes

Introduction -- Roots of commutative algebra -- Localization -- Associated primes and primary decomposition -- Integral dependence and the nullstellensatz -- Filtrations and the Artin-Rees Lemma -- Flat families -- Completions and Hensel's Lemma -- Introduction to dimension theory -- Fundamental definitions of dimension theory -- The principal ideal theorem and systems of parameters -- Dimension and codimension one -- Dimension and Hilbert-Samuel Polynomials -- The dimension of affine rings -- Elimination theory, generic freeness, and the dimension of fibers -- Gröbner bases -- Modules of differentials -- Regular sequences and the Koszul complex -- Depth, codimension, and Cohen-Macaulay rings -- Homological theory of regular local rings -- Free resolutions and fitting invariants -- Duality, canonical modules, and Gorenstein rings