Mart ABEL, Mati ABEL

Traces of Maximal Ideals of Topological Algebras in Their Subalgebras

Let K be one of the fields R or C, A a topological associative algebra over K with separately continuous multiplication, B a subalgebra of A and M a closed maximal regular left (right or two-sided) ideal of A such that the trace M \cap B of M is a proper subset of B. In cases, when B is a Gelfand-Mazur subalgebra of A or a subalgebra of the centre Z(A) of A, such classes of topological algebras in which M \cap B (in the subset topology) is a closed maximal regular left (respectively, right or two-sided) ideal of B, are described.

Anahtar Kelimeler:

Topological algebras, Gelfand-Mazur algebras, locally pseudoconvex algebras, galbed algebras, traces of ideals in subalgebras

Traces of Maximal Ideals of Topological Algebras in Their Subalgebras

Keywords:

Topological algebras, Gelfand-Mazur algebras, locally pseudoconvex algebras, galbed algebras, traces of ideals in subalgebras,

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