An ideal in a commutative topological algebra with separately continuous multiplication is non-removable if and only if it consists locally of joint topological divisors of zero. Also, any family of non-removable ideals can be removed simultanously.
@article{urn:eudml:doc:42515, title = {Non-removable ideals in commutative topological algebras with separately continuous multiplication.}, journal = {Collectanea Mathematica}, volume = {42}, year = {1991}, pages = {189-198}, zbl = {0793.46033}, mrnumber = {MR1203180}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42515} }
Müller, Vladimir. Non-removable ideals in commutative topological algebras with separately continuous multiplication.. Collectanea Mathematica, Tome 42 (1991) pp. 189-198. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42515/