Idéaux non removables dans la classe des algèbres bornologiques multiplicativement convexes

Abstract

This paper is a continuation of [2], [9] and [10]. Its aim is to characterize non-removable ideals in the class ${\cal M}$ of all multiplicatively convex bornological algebras. Let $A$ be in ${\cal M}$. We show that an ideal $I\subset A$ is ${\cal M}$-non-removable if and only if it consists of joint m-bounding elements (D\'ef. 9). Such an ideal doesn't consist, in general, of joint bounding elements (D\'ef. 8). This shows that the concept of ${\cal M}$-non-removable ideals is of relative character (D\'ef. 4).