We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-2-4,
author = {W. \.Zelazko},
title = {A characterization of F-algebras with all one-sided ideals closed},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {135-145},
zbl = {1074.46031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-2-4}
}
W. Żelazko. A characterization of F-algebras with all one-sided ideals closed. Studia Mathematica, Tome 166 (2005) pp. 135-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-2-4/