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/