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| Introduction 1.Basic Properties in Commutative Algebra 2.Tree Structure 3.Ultrametric Absolute Values 4.L-Productal Vector Spaces 5.Multiplicative Semi-Norms and Shilov Boundary 6.Spectral Semi-Norm 7.Hensel Lemma 8.Infraconnected Sets 9.Monotonous Filters 10.Circular Filters 11.Tree Structure and Metric on Circular Filters 12.Rational Functions and Algebras R(D) 13.Simple Convergence on Mult(K[x]) 14.Topologies on Mult(g[x]) 15.Spectral Properties and Gelfand Transforms 16.Analytic Elements 17.Holomorphic Properties on Infraconnected Sets 18.T-Filters and T-Sequences 19.Applications of T-Filters and T-Sequences 20.Analytic Elements on Classic Partitions 21.Holomorphic Properties on Partitions 22.Shilov Boundary for Algebras H(D, (9) 23.Holomorphic Functional Calculus 24.Uniform K-Banach Algebras and Properties (s)and (q) 25.Properties (o) and (q) in Uniform Banach K-Algebras 26.Properties (o) and (q) and Strongly Valued Fields 27.Multbijective Banach K-Algebras 28.Pseudo-Density of Multi(A, II . II) 29.Polnorm on Algebras and Algebraic Extensions 30.Definition of Affinoid Algebras 31.Algebraic Properties of Affinoid Algebras 32.Jacobson Radical of Affinoid Algebras 33.Salmon's Theorems 34.Separable Fields 35.Spectral Norm of Affinoid Algebras 36.Spectrum of an Element of an Affinoid Algebra 37.Krasner-Tate Algebras 38.Universal Generators in Tate Algebras 39.Mappings from H(D) to the Tree Uult(K[x]) …… References Definitions Index Notation Index |
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