One-Dimensional Cohen-Macaulay Rings |
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hDivisible and Cotorsion Modules | 1 |
Chapter II | 11 |
Chapter III | 28 |
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A₁ Artinian divisible R-module Artinian R-module assume B₁ canonical ideal closed component Cohen-Macaulay ring commutative ring completion composition series contains Corollary 1.3 cotorsion R-module D₁ direct sum discrete valuation ring domain of Krull epimorphism exact sequence finite length finitely generated R-module full ring Gorenstein ring h-divisible h-reduced Hence by Theorem homomorphic image Homp ideal of H ideal of rank injective R-module integral closure integral domain isomorphic Ker f Krull dimension Lemma local ring M-primary ideal maximal ideal Noetherian local domain Noetherian ring one-to-one correspondence P-primary component P₁ prime ideal pseudo valuation rings R-homomorphism R-topology regular element regular ideal ring of quotients series of divisible simple divisible R-module simple divisible submodule statements are equivalent strongly unramified ring superficial element superficial of degree Suppose Theorem 6.6 torsion R-module torsion-free and divisible torsion-free R-module unmixed ideal unramified ring extension V₁