It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.
@article{bwmeta1.element.doi-10_2478_s11533-012-0041-7,
author = {Mati Abel},
title = {Topological algebras with maximal regular ideals closed},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1054-1059},
zbl = {1250.46033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0041-7}
}
Mati Abel. Topological algebras with maximal regular ideals closed. Open Mathematics, Tome 10 (2012) pp. 1054-1059. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0041-7/
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