(Mostly) commutative algebra

著者

• Chambert-Loir, Antoine

書誌事項

(Mostly) commutative algebra

Antoine Chambert-Loir

（Universitext）

Springer, c2021

注記

Includes bibliographical references (p. 455-457) and index

内容説明・目次

内容説明

This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.

目次

Preface.- 1 Rings.- 2 Ideals and divisibility.- 3 Modules.- 4 Field extensions.- 5 Modules over principal ideal rings.- 6 Noetherian and artinian rings. Primary decomposition.- 7 First steps in homological algebra.- 8 Tensor products and determinants.- 9 Commutative algebra: the normalization theorem, dimension theory, Dedekind rings.- Appendix.- References.- Index.-

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BC06942749
• ISBN:
  • 9783030615949
• 出版国コード: sz
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cham
• ページ数/冊数: xv, 466 p.
• 大きさ: 24 cm
• 分類:
  • DC23 : 512.44
• 件名:
  • LCSH : Commutative algebra
• 親書誌ID:
  • BA00021004