A Primer of Commutative Algebra

A Primer of Commutative Algebra

Language: English

by Milne James S.

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Categories

Commutative Algebra

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.