About this product

Product Identifiers

PublisherCambridge University Press

ISBN-100521480728

ISBN-139780521480727

eBay Product ID (ePID)536518

Product Key Features

Number of Pages244 Pages

Publication NameAlgebraic Introduction to Complex Projective Geometry Vol. 1 : Commutative Algebra

LanguageEnglish

Publication Year1996

SubjectAlgebra / General, Geometry / Algebraic, Complex Analysis

TypeTextbook

Subject AreaMathematics

AuthorChristian Peskine

SeriesCambridge Studies in Advanced Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.7 in

Item Weight16 Oz

Item Length9.3 in

Item Width6.2 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN94-046980

Reviews"Useful, apt advice and numerous expository niceties make this compact volume a pleasure to read. Highly recommended." Choice, "...a good and systematic introduction to complex projective geometry....an excellent textbook." Mathematical Reviews

Dewey Edition20

TitleLeadingAn

Series Volume NumberSeries Number 47

Dewey Decimal516/.5

Table Of Content1. Rings, homomorphisms, ideals; 2. Modules; 3. Noetherian rings and modules; 4. Artinian rings and modules; 5. Finitely generated modules over Noetherian rings; 6. A first contact with homological algebra; 7. Fractions; 8. Integral extensions of rings; 9. Algebraic extensions of rings; 10. Noether's normalisation lemma; 11. Affine schemes; 12. Morphisms of affine schemes; 13. Zariski's main theorem; 14. Integrally closed Noetherian rings; 15. Weil divisors; 16. Cartier divisors; Subject index; Symbols index.

SynopsisIn this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra., An excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra., In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra., This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory.

LC Classification NumberQA564 .P47 1996