Introduction to Commutative Algebra
Introduction to Commutative Algebra is a well-known commutative algebra textbook written by Michael Atiyah and Ian G. Macdonald. It is on the list of 173 books essential for undergraduate math libraries. [1] As of May 2025, Google Scholar 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 textbooks in the subject, relegating a good deal of material to the exercises.
(Hardcover 1969, ISBN 0-201-00361-9) (Paperback 1994, ISBN 0-201-40751-5)
Reviews
[edit]Michael Berg says "this classic book, is one of the premier texts for a serious graduate (or very gifted undergraduate) student".[2] Mark Green calls it an "elegant minimalist introduction". [3] W. Jonsson says "An amazing amount of information is included in the 128 pages of this book". [4] 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". [5] 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."
References
[edit]- ^ "The Basic Library List: MAA's Recommendations for Undergraduate Libraries". 4 November 2022. Retrieved 24 May 2025.
- ^ Berg, Michael. "Introduction to Commutative Algebra". Mathematical Association of America (MAA). Retrieved 2025-05-23.
- ^ Green, Mark (1996). "Commutative algebra with a view toward algebraic geometry". Bulletin of the American Mathematical Society. 33 (3): 367.
- ^ Jonsson, Wilbur (1970). "Introduction to Commutative algebra". Canadian Mathematical Bulletin. 13: 162.
- ^ Lewis, D.J.; McDonald, B.R. (1970). "Introduction to Commutative Algebra". The American Mathematical Monthly. 77 (7): 783–784.
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