Commutative Rings: Course Notes for 18.732, Spring, 1966, M.I.T.

a₁ abelian group algebra assertion associated prime b₁ closed point closed set closed subsets closure cocycles coefficients cohomology cokernel commutative completes the proof contains coprimary Corollary corresponding dedekind domain denote diagram discrete valuation ring equation exact sequence extension faithfully flat field of fractions finite presentation finite set finite type follows fractional ideal free module functor hence homomorphism Homp injective integral domain integrally closed intersection invertible kernel Krull LEFT EXACTNESS lemma local ring M₁ map f maximal ideal minimal primes module of finite noetherian ring notation open sets P₁ polynomial ring PRESHEAF prime ideal Proposition quasi-coherent R-algebra R-module R₁ rank residue RIGHT EXACTNESS RING OF FRACTIONS s-¹M s-¹R s¯¹R S₁ scalars SECTION Spec spectrum stalk structure submodule supp Suppose surjective tensor product theorem topological space twisted forms U₁ unique unit ideal universal property X₁ ΑΠΑ