書誌事項

Commutative algebra

Christian Peskine

(Cambridge studies in advanced mathematics, 47 . An algebraic introduction to complex projective geometry ; 1)

Cambridge University Press, 1996

  • : hdk

大学図書館所蔵 件 / 全67件

この図書・雑誌をさがす

注記

Includes bibliography (p. 223), and subject and symbols indexes

内容説明・目次

内容説明

In 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.

目次

  • 1. 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.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

ページトップへ

AltStyle によって変換されたページ (->オリジナル) /