Course in commutative algebra
Kemper, Gregor,
Course in commutative algebra Gregor Kemper. - New York : Springer, c2011. - xi, 246 p. : ill. ; 25 cm. - Graduate texts in mathematics, 256 0072-5285 ; . - Graduate texts in mathematics ; 256. .
Includes bibliographical references (p. 235-237) and indexes.
Introduction ---- Part I. The Algebra-Geometry Lexicon. 1. Hilbertʹs 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. Grobner 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 ---- Solutions of Some Exercises.
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.--
9783642035449 (Hbk) Euro 26.99 = Mathematics-reference book collection
2013444043
09,N40,0568 dnb
996813195 DE-101 015392058 Uk
Commutative algebra.
Algebra.
Mathematics.
Àlgebra commutativa.
Matemàtica.
Kommutative Algebra
QA251.3 / .K456 2011
516.35 K32C
Course in commutative algebra Gregor Kemper. - New York : Springer, c2011. - xi, 246 p. : ill. ; 25 cm. - Graduate texts in mathematics, 256 0072-5285 ; . - Graduate texts in mathematics ; 256. .
Includes bibliographical references (p. 235-237) and indexes.
Introduction ---- Part I. The Algebra-Geometry Lexicon. 1. Hilbertʹs 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. Grobner 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 ---- Solutions of Some Exercises.
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.--
9783642035449 (Hbk) Euro 26.99 = Mathematics-reference book collection
2013444043
09,N40,0568 dnb
996813195 DE-101 015392058 Uk
Commutative algebra.
Algebra.
Mathematics.
Àlgebra commutativa.
Matemàtica.
Kommutative Algebra
QA251.3 / .K456 2011
516.35 K32C