## Examples of Commutative Rings |

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Awesome book, an unsung hero, a diamond in the rough. I've used it for 20 years. 167pp = not worth $200 price some ask. Check out a copy and leave it near the xerox room ...

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1-dimensional abelian group actually addition algebraic Amer ascending chain Bézout called catenary clearly closure Cohen-Macaulay completely integrally closed consider consisting construction contained Dedekind domain defined definition denoted dim(R dim(T dimension direct divisible divisor elements equivalent Exercise exists fact factorial domain fail finitely flat follows fractional ideal functions Gilmer given Gorenstein height Hilbert domain infinite infinite-dimensional injective instance integrally closed domain interest intersection invertible irreducible isomorphic Kaplansky 1974b Krull domain localization lying Math maximal ideal minimal module multiplication nilpotent Noetherian ring Noetherian valuation domain non-Noetherian nonzero elements Notice numbers OOOOO Example possible prime ideal principal ideal domain projective proof Prüfer domain quasi-local quotient field R-module radical regular respectively satisfies sequence Specifically subgroups subring Suppose theorem topology union unique units valuation domain