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Chapter IINOETHERIAN RINGS AND MODULES
Chapter IIINTEGRAL EXTENSIONS AND DEDEKIND
algebraic set Applying arbitrary Artin Ass(M associated assume assumption belongs called coefficients commutative completion condition consequently consider consists contained Corollary correspondence Dedekind domain defined definition denote determined discrete valuation ring Div(R divisor easily element equality equation equivalent exact Example Exercises exists exists an element extension field finitely finitely generated R-module follows formula fractional ideal function given graded height Hence homogeneous homomorphism implies important inclusion induces integral integral closure intersection invertible irreducible irredundant isomorphism Krull domain Lemma linear mapping Mathematics maximal ideal minimal module multiplicative natural Noetherian ring non-zero element normal Observe obtain Obviously operations polynomial ring positive primary decomposition prime ideal principal Proof properties prove R-module relation respect result satisfies the condition sequence Spec(R submodule subring subset Suppose Theorem theory topology whence write yields zero