A Primer of Commutative Algebra

A Primer of Commutative Algebra

Commutative Algebra

Milne James S.

Published on Oct 11th 2011


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.


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.

75 pages

0.5 mb