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Journals / Turkish Journal of Mathematics / 2004 / Cilt: 28 - Sayı: 4

Ideal Theory in Topological Algebras

Abdelhak NAJMI

Pages
313–333
DOI
—

Abstract

Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set \mathcal{X}(A), of all continuous multiplicative linear functionals, is not empty.

Özet

Given a simplicial topologically non radical algebra A, we characterize its topological radical, radA. If furthermore A is advertive, then radA coincides with the Jacobson radical RadA. On the other hand, it is shown that every two-sided invertive simplicial topological Gelfand-Mazur algebra has a functional spectrum and for every topologically nonradical simplicial Gelfand-Mazur amits the set \mathcal{X}(A), of all continuous multiplicative linear functionals, is not empty.

Keywords: Left, right or two-sidedness, commutativity, almost commutativity, aits, alits, arits, amits, almits, armits, topological algebra, simplicial algebra, advertive or invertive algebra, radical, topological radical, Gelfand-Mazur algebra