Kemper, Gregor.
A Course in Commutative Algebra [electronic resource] / by Gregor Kemper. - XII, 248 p. online resource. - Graduate Texts in Mathematics, 256 0072-5285 ; . - Graduate Texts in Mathematics, 256 .
Introduction -- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz; 2 Noetherian and Artinian Rings; 3 The Zariski Topology; 4 A Summary of the Lexicon -- Part II Dimension: 5 Krull Dimension and Transcendence Degree; 6 Localization; 7 The Principal Ideal Theorem; 8 Integral Extensions -- Part III Computational Methods: 9 Gröbner Bases; 10 Fibers and Images of Morphisms Revisited; 11 Hilbert Series and Dimension -- Part IV Local Rings: 12 Dimension Theory; 13 Regular Local Rings; 14 Rings of Dimension One -- References -- Notation -- Index.
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
9783642035456
10.1007/978-3-642-03545-6 doi
Mathematics.
Geometry, algebraic.
Algebra.
Computer science--Mathematics.
Mathematics.
Algebraic Geometry.
Commutative Rings and Algebras.
Computational Mathematics and Numerical Analysis.
QA564-609
516.35
A Course in Commutative Algebra [electronic resource] / by Gregor Kemper. - XII, 248 p. online resource. - Graduate Texts in Mathematics, 256 0072-5285 ; . - Graduate Texts in Mathematics, 256 .
Introduction -- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz; 2 Noetherian and Artinian Rings; 3 The Zariski Topology; 4 A Summary of the Lexicon -- Part II Dimension: 5 Krull Dimension and Transcendence Degree; 6 Localization; 7 The Principal Ideal Theorem; 8 Integral Extensions -- Part III Computational Methods: 9 Gröbner Bases; 10 Fibers and Images of Morphisms Revisited; 11 Hilbert Series and Dimension -- Part IV Local Rings: 12 Dimension Theory; 13 Regular Local Rings; 14 Rings of Dimension One -- References -- Notation -- Index.
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
9783642035456
10.1007/978-3-642-03545-6 doi
Mathematics.
Geometry, algebraic.
Algebra.
Computer science--Mathematics.
Mathematics.
Algebraic Geometry.
Commutative Rings and Algebras.
Computational Mathematics and Numerical Analysis.
QA564-609
516.35