''Introduction to Commutative Algebra'' is a well-known
commutative algebra
Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...
textbook written by
Michael Atiyah and
Ian G. Macdonald. It is on the list of 173 books essential for undergraduate math libraries.
As of May 2025,
Google Scholar
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lists over 8000 citations to this book.
It deals with elementary concepts of commutative algebra including
localization,
primary decomposition,
integral dependence,
Noetherian and
Artinian rings and
modules,
Dedekind rings,
completions and a moderate amount of
dimension theory. It is notable for being among the shorter English-language introductory
textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions, but also of learners ( ...
s in the subject, relegating a good deal of material to the
exercise
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s.
(Hardcover 1969, ) (Paperback 1994, )
Reviews
Michael Berg says "this classic book, is one of the premier texts for a serious graduate (or very gifted undergraduate) student".
Mark Green calls it an "elegant minimalist introduction". W. Jonsson says "An amazing amount of information is included in the 128 pages of this book".
D. J. Lewis says "The highlight of the text is the very excellent set of problems which constitute one-third of the text". B. R. McDonald says "The student consensus was that the text was very readable ... we were pleased with the success of the text".
On the other hand, Lewis says "The text is very tersely written, examples are a bit scarce and proofs are condensed. This reviewer doubts that many students can profitably read it unassisted."
The book has enthusiastic endorsements from several math professors. Henry Pinkham, former Professor of Math at Columbia University said "probably the best introduction to Commutative Algebra, and has very good exercises." Jonathan Wise, Associate Professor at University of Colorado Boulder says "may be the best math textbook ever written."
References
1969 non-fiction books
Mathematics textbooks
Commutative algebra
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