Commutative Noetherian and Krull Rings |
Contents
Preface | 7 |
Chapter IINOETHERIAN RINGS AND MODULES | 49 |
Chapter IIIINTEGRAL EXTENSIONS AND DEDEKIND | 104 |
Copyright | |
2 other sections not shown
Common terms and phrases
a₁ algebraic set Artin ring Ass(M b₁ belongs class group coefficients contained Corollary Dedekind domain defined definition denote discrete valuation ring div(I Div(j Div(R divisor epimorphism equality exact sequence exist elements exists an element field of fractions field Ro finite number finitely generated R-module formula fractional ideal free module function graded ring Hence I-adic topology I₁ ideal Q implies inclusion induces integral closure intersection invertible irreducible irredundant primary decomposition isomorphism Krull domain Lemma linear m₁ mapping maximal ideal monomorphism morphism multiplicative subset nilpotent Noetherian domain Noetherian ring non-zero element non-zero ideal non-zero prime ideal P₁ polynomial ring positive integer primary decomposition primary ideals prime numbers Prin(R principal ideal Proof properties prove Q₁ R₁ rad(Q ring of fractions ring of polynomials ring Rp s₁ satisfies the condition Section Spec(R Spec¹ submodule subring Supp(M t₁ unique factorization domain whence X₁ zero-divisor αελ