Characterizations of \(Q\)-algebras of type \(F\) and of \(F\)-algebras with all ideals closed (Q2765275)

The main topic of this paper is the question when a commutative Fréchet algebra has all ideals closed. The author proves that a commutative Fréchet algebra \(A\) has all ideals closed if and only if it is a Noetherian algebra and a \(Q\)-algebra. Also, it is noticed, using a result of Akkar and Nacir, that a commutative Noetherian Fréchet algebra \(A\) is a \(Q\)-algebra. Examples are given to show that the result does not hold for complete non-metrizable topological algebras and for incomplete normed \(Q\)-algebras which are not Noetherian.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00059].