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abelian group Abstract algebra Amer AMS Subject Classification artinian classical quotient assume automorphism Banach space bounded Canadian Mathematical Society classical quotient ring coefficients commutative compactification condition contains continuous convergence convex Corollary countable Dedekind defined denote Department of Mathematics differential equation editors element equivalent exists finite follows function graph group G group rings Hence homomorphism homotopy implies induced integral domain invariant isometry isomorphism lattice Lemma lemme Let G linear Math Mathematical Society 1984 measure min-p nilpotent Noetherian non-zero nonsingular norm normal normal subgroup obtain operator orthogonal orthogonal polynomials oval p-large subgroup points polynomials positive integer positive solution prime ideal prime ring proof of Theorem Proposition prove quotient ring Remark result retract revised form Riesz pseudonorm Riesz space satisfies semilattice sequence spectral split graph subgroup of G subset subspace Suppose theory topological space type-R U(KG valuation domain zero