''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 ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent ...
textbook written by
Michael Atiyah
Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded ...
and
Ian G. Macdonald
Ian Grant Macdonald (born 11 October 1928 in London, England) is a British mathematician known for his contributions to symmetric functions, special functions, Lie algebra theory and other aspects of algebra, algebraic combinatorics, and combi ...
. It deals with elementary concepts of commutative algebra including
localization,
primary decomposition
In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many ''primary ideals'' (which are relate ...
,
integral dependence,
Noetherian In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects, meaning that certain ascending or descending sequences of subobjects must have finite lengt ...
and
Artinian rings
Ring may refer to:
* Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry
* To make a sound with a bell, and the sound made by a bell
:(hence) to initiate a telephone connection
Arts, entertainment and media Film an ...
and
modules
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a sy ...
,
Dedekind ring
In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessaril ...
s,
completions and a moderate amount of
dimension theory
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordin ...
. 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. Schoolbooks are textbook ...
s in the subject, relegating a good deal of material to the
exercise
Exercise is a body activity that enhances or maintains physical fitness and overall health and wellness.
It is performed for various reasons, to aid growth and improve strength, develop muscles and the cardiovascular system, hone athletic ...
s.
(Hardcover 1969, ) (Paperback 1994, )
1969 non-fiction books
Mathematics textbooks
Commutative algebra
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