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A Course in Commutative Algebra

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...

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Bibliographic Details
Main Author: Kemper, Gregor. (Author, http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Edition:1st ed. 2011.
Series:Graduate Texts in Mathematics, 256
Subjects:
Algebraic geometry.
Commutative algebra.
Commutative rings.
Computer mathematics.
Algebraic Geometry.
Commutative Rings and Algebras.
Computational Mathematics and Numerical Analysis.
Online Access:https://doi.org/10.1007/978-3-642-03545-6
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245 1 2 |a A Course in Commutative Algebra  |h [electronic resource] /  |c by Gregor Kemper. 
250 |a 1st ed. 2011. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2011. 
300 |a XII, 248 p.  |b online resource. 
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490 1 |a Graduate Texts in Mathematics,  |x 0072-5285 ;  |v 256 
505 0 |a 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. 
520 |a 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. 
650 0 |a Algebraic geometry. 
650 0 |a Commutative algebra. 
650 0 |a Commutative rings. 
650 0 |a Computer mathematics. 
650 1 4 |a Algebraic Geometry.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/M11019 
650 2 4 |a Commutative Rings and Algebras.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/M11043 
650 2 4 |a Computational Mathematics and Numerical Analysis.  |0 https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 
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773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783642035876 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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