Topics in Commutative Ring Theory |
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Page 50
... two - dimensional regular local ring . Let X , Y be a minimal base for the maximal ideal M R. Let T = R [ y / x ] . We have that MT = XT of Then T is globally regular and factorial and that this ideal is prime . T has an height infinite ...
... two - dimensional regular local ring . Let X , Y be a minimal base for the maximal ideal M R. Let T = R [ y / x ] . We have that MT = XT of Then T is globally regular and factorial and that this ideal is prime . T has an height infinite ...
Page 51
... regular two - dimensional local ring . Theorem 268. Let RCR CR2 ... be a sequence of domains with Ro two - dimensional regular and each Ri + 1 an immediate quadratic extension of R. R ; Then R is a valuation domain . UR ; Proof ...
... regular two - dimensional local ring . Theorem 268. Let RCR CR2 ... be a sequence of domains with Ro two - dimensional regular and each Ri + 1 an immediate quadratic extension of R. R ; Then R is a valuation domain . UR ; Proof ...
Page 53
... 2 . By altitude formula facts , T / N is finite - dimensional over R / M . By Zariski's main theorem , local style , there is a contradiction . Theorem 270. Let R be a two - dimensional regular local ring , and T a two - dimensional regular ...
... 2 . By altitude formula facts , T / N is finite - dimensional over R / M . By Zariski's main theorem , local style , there is a contradiction . Theorem 270. Let R be a two - dimensional regular local ring , and T a two - dimensional regular ...
Common terms and phrases
1817 LIBRARIES A/XA a₁ analytically unramified annihilator antichains argument Artin-Rees lemma Artinian modules ascending chain condition assume closed set coefficients commutative ring contradiction countable deduce degree domain with quotient equation exists finite number finitely generated ideal finitely generated R-module graded ring height Hence homogeneous element homomorphic image ideals containing indeterminates induction integral closure integrally closed domain intersection isomorphic J-ideals Krull dimension M-primary Macaulay module maximal ideal MICHIG MICHIGAN CHIGAN minimal prime ideal neocommutative Noetherian ring non-zero-divisor number of elements number of prime P₁ partially ordered set Pick principal ideal principal prime proof of Theorem prove quasi-local quotient field R-sequence R₁ R₂ radical ideal regular local ring Remark sequence set of prime submodule subring subset Suppose Theorem 247 Theorem 306 two-dimensional regular U₁ UNIV UNIVERSITY valuation domain VERSITY Write X₁ zero-divisors ε Ι