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LMSST: 51 Steps Commut Algebra 2ed 2nd Edition
Author(s): Sharp (Author)
- Publisher: Cambridge University Press
- Publication Date: 12 Jan. 2008
- Edition: 2nd
- Language: English
- Print length: 368 pages
- ISBN-10: 0521646235
- ISBN-13: 9780521646239
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.
Editorial Reviews
Review
‘… 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, The Mathematical Gazette
Book Description
Introductory account of commutative algebra, aimed at students with a background in basic algebra.
