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Ideal Theory In Topological Algebras, A. Najmi

Turkish Journal of Mathematics

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.