A Course in Commutative Algebra

• Κύριος συγγραφέας: Kemper, Gregor (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Σειρά: Graduate Texts in Mathematics, 256
• Θέματα: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Computer mathematics.; Algebraic Geometry.; Commutative Rings and Algebras.; Computational Mathematics and Numerical Analysis.

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 mainta...

Πίνακας περιεχομένων:

• 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.