pdf (current version 2.22, March 30, 2011).
Abstract
These notes prove the basic theorems in commutative
algebra required for algebraic geometry and algebraic
groups. They assume only a knowledge of the algebra usually
taught in advanced undergraduate or first-year graduate
courses. However, they are quite concise.
Contents
Rings and algebras; ideals; noetherian rings; unique factorization; integrality;
rings of fractions; direct limits; tensor products;
flatness; finitely generated projective modules; the Hilbert Nullstellsatz; the max spectrum of a ring;
dimension theory for finitely generated
k-algebras;
primary decompositions; artinian rings; dimension theory for noetherian rings;
regular local rings; connections with geometry.
History
v1.00 (January 1, 2009). First version on the web. 51 pages.
pdf (old version 1.00).
v2.00 (April 5, 2009). Revised and completed. 64 pages.
pdf (old version 2.00).
v2.10 (May 30, 2009). Many improvements to the exposition (thanks to Shu Otsuka). 65 pages.
pdf (old version 2.10).
v2.20 (April 10, 2010). Added section on finitely generated projective modules; minor fixes.74 pages.
pdf (old version 2.20).
v2.21 (April 27, 2010). Minor fixes. 74 pages.
pdf (old version 2.21).
v2.22 (March 30, 2011). Minor changes. 75 pages.