Introduction To Commutative AlgebraThis book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read |
Contents
Modules | 17 |
Rings and Modules of Fractions | 36 |
Primary Decomposition | 50 |
Copyright | |
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Common terms and phrases
A-algebra A-bilinear a-filtration A-module homomorphism a-topology a₁ abelian group Artin ring Artinian Chapter coefficients commutative algebra composition series coprime Corollary Dedekind domain Deduce defined denote dimension example Exercise exists field of fractions finitely generated A-module finitely-generated A-module following are equivalent fractional ideal graded ring Hausdorff hence homomorphism f induces injective integral domain integrally closed intersection inverse irreducible isomorphism Jacobson radical lemma Let f let p₁ m/mē M₁ mapping f maximal element maximal ideal minimal primary decomposition minimal prime ideal module morphism multiplicatively closed subset nilpotent nilradical Noetherian local ring Noetherian ring open sets p-primary polynomial ring power series primary decomposition primary ideals prime ideals belonging Proof Proposition Prove q₁ quotient resp ring and let ring homomorphism satisfies Show Spec submodule subring Suppose surjective tensor product Theorem topology u₁ unique vector space x₁ y₁ zero-divisor