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  1. Home
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  3. Steps in Commutative Algebra
  • Cited by 19
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2001
Online ISBN:
9780511623684
DOI:
https://doi.org/10.1017/CBO9780511623684
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
London Mathematical Society Student Texts (51)
Information

Book 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.

Reviews

‘… a very useful stepping-stone for students in their study of commutative algebra.’

H. Mitsch - Universität Wien

'… Sharp is an excellent guide, clearly aiming never to leave his readers floundering … This standard of care for his readers is maintained throughout the book … this is a superb guide to an attractive and important area of mathematics, and one from which I will derive pleasure as a retirement project. But it will never be an easy ride.'

John Baylis Source: The Mathematical Gazette

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