Commutative algebra, with a view toward algebraic geometry

Front Matter....Pages i-xvi
Introduction....Pages 1-10
Elementary Definitions....Pages 11-17
Front Matter....Pages 19-19
Roots of Commutative Algebra....Pages 21-56
Localization....Pages 57-86
Associated Primes and Primary Decomposition....Pages 87-115
Integral Dependence and the Nullstellensatz....Pages 117-144
Filtrations and the Artin-Rees Lemma....Pages 145-153
Flat Families....Pages 155-178
Completions and Hensel’s Lemma....Pages 179-209
Front Matter....Pages 211-211
Introduction to Dimension Theory....Pages 213-224
Fundamental Definitions of Dimension Theory....Pages 225-229
The Principal Ideal Theorem and Systems of Parameters....Pages 231-246
Dimension and Codimension One....Pages 247-269
Dimension and Hilbert-Samuel Polynomials....Pages 271-280
The Dimension of Affine Rings....Pages 281-301
Elimination Theory, Generic Freeness, and the Dimension of Fibers....Pages 303-315
Gröbner Bases....Pages 317-381
Modules of Differentials....Pages 383-415
Front Matter....Pages 417-417
Regular Sequences and the Koszul Complex....Pages 419-446
Depth, Codimension, and Cohen-Macaulay Rings....Pages 447-468
Front Matter....Pages 417-417
Homological Theory of Regular Local Rings....Pages 469-488
Free Resolutions and Fitting Invariants....Pages 489-517
Duality, Canonical Modules, and Gorenstein Rings....Pages 519-554
Back Matter....Pages 555-788