Topics in Commutative Ring Theory |
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