On ideals consisting of topological zero divisors (Q2717538)

Let \(A\) be a commutative Banach algebra over \(\mathbb{C}\). The notion of joint topological divisors of an ideal \(I\subset A\) (joint TZD) is introduced. The main theorem states:NEWLINENEWLINENEWLINELet \(A\) be unital. If \(J\subset A\) is an ideal consisting of TZD then there is in \(A\) a maximal ideal \(I\) also consisting of TZD such that \(J\subset I\).NEWLINENEWLINENEWLINEThis extends certain result of \textit{Z. Słodkowski} [ibid. 48, 83-88 (1973; Zbl 0271.46046)].