Steps in commutative algebra
By: R.Y. Sharp.
Edition: 2nd ed.
Series: London Mathematical Society student texts ;; 51
Publisher: Cambridge University Press
Published: 2000
Place of publication: Cambridge, UK; New York
Language: eng
Number of pages: 355
Subjects: Commutative algebra.
Description: This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.
Notes: Includes bibliographical references (p. 345-346) and index.