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abelian groups Abstract algebra Amer applied assume asymptotic Banach space bounded central limit theorem coefficients complete condition congruence consider constant contains continued fraction continuous convergence convex coordinates corresponding cross ratio curvature curve defined definition denote derivatives determined differential equations double points elements equivalent exists field finite number following theorem formula Fourier series function geodesic given Hence homeomorphism hypersurfaces ideal inequality infinite integer integral intersection invariant Irving Kaplansky isomorphic Lemma linear mapping Math mathematical matrix mean curvature method metric obtained p-adic paper plane polynomials power series prime problem Professor professorship proof properties proved quadratic quadratic forms quadrics rational Received Reinhold Baer relation respect result ring satisfy sequence solution space subgroup subset summability surface tangent theory tion topological topological spaces transformation University valuation variables vector zero