Turkish Journal of Mathematics
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.
Topological algebras, Gelfand-Mazur algebras, locally pseudoconvex algebras, galbed algebras, traces of ideals in subalgebras
ABEL, MART and ABEL, MATI (2007) "Traces of Maximal Ideals of Topological Algebras in Their Subalgebras," Turkish Journal of Mathematics: Vol. 31: No. 1, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol31/iss1/6