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Commutative algebra with a view toward algebraic geometry /
Eisenbud, David
Commutative algebra with a view toward algebraic geometry / David Eisenbud - Corr. 3rd print - xvi, 797 pages : illustrations ; 24 cm - Graduate texts in mathematics ; 150 . - Graduate texts in mathematics ; 150 .
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
0387942696 9780387942698 0387942688 9780387942681 3540942696 9783540942696
Commutative algebra
Geometry, Algebraic
QA251.3 / .E38 2004
Commutative algebra with a view toward algebraic geometry / David Eisenbud - Corr. 3rd print - xvi, 797 pages : illustrations ; 24 cm - Graduate texts in mathematics ; 150 . - Graduate texts in mathematics ; 150 .
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
0387942696 9780387942698 0387942688 9780387942681 3540942696 9783540942696
Commutative algebra
Geometry, Algebraic
QA251.3 / .E38 2004
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