PICARD-BOREL ALGEBRAS
Language
en
Document de travail - Pré-publication
English Abstract
A Picard-Borel algebra is a commutative, unital, complex algebra A such that every family (u λ) λ∈Λ of invertible elements of A which are pairwise linearly independent is linearly independent. A Picard-Borel algebra is ...Read more >
A Picard-Borel algebra is a commutative, unital, complex algebra A such that every family (u λ) λ∈Λ of invertible elements of A which are pairwise linearly independent is linearly independent. A Picard-Borel algebra is said to be nontrivial if u / ∈ C1 for some invertible element u ∈ A. The algebra C[X] of complex polynomials is an obvious example of trivial Picard-Borel algebra, and results from the celebrated 1897 paper "Sur les zéros des fonctions entières" by E. Borel show that the algebra H(C) of entire functions on C is a Picard-Borel algebra. The main result of the paper shows that Picard-Borel algebras which are Fréchet algebras are integral domains.Read less <
Origin
Hal imported