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Chapter DNOETHERIAN RINGS AND MODULES
Chapter HIINTEGRAL EXTENSIONS AND DEDEKIND
2 other sections not shown
adic topology algebraic set Artin module Artin ring belongs called coefficients commutative consequently contained Corollary Dedekind domain defined Definition denote discrete valuation ring element r e epimorphism equality exact sequence exist elements exists an element field of fractions field R0 finite number finitely generated module follows from Theorem formula fractional ideal free module graded ring Hence ideal Q ideals Pt implies inclusion indeterminates induces integral closure intersection irredundant primary decomposition isomorphism Krull domain Lemma mapping Mathematics maximal ideal monomorphism morphism multiplicative subset nilpotent Noetherian domain Noetherian ring non-zero element non-zero ideal non-zero prime ideal number theory obtain polynomial ring positive integer primary decomposition primary ideals prime numbers Proof Let properties prove residue classes ring K[Xt ring of fractions ring of polynomials satisfies the condition Section Spec Spec1 submodule subring Suppose unique factorization domain whence x e R0 Z-module zero zero-divisor