Turkish Journal of Mathematics
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.
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
First Page
313
Last Page
334
Recommended Citation
NAJMI, A. (2004) "Ideal Theory in Topological Algebras," Turkish Journal of Mathematics: Vol. 28: No. 4, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol28/iss4/1
