When is \(C(X)\) polynomially ideal?
For an \(f\)-algebra and an ideal \(\mathfrak a\), a notion of being polynomially \(\mathfrak a\)-ideal is introduced. It is shown that if the algebra is bounded inversion closed and \(\mathfrak a\) is an intersection of maximal ideals, this notion is equivalent to idempotents lifting modulo \(\mathfrak a\). For spaces of continuous functions on a Tychonoff space, the notion is then linked to the space being a \(P\)-space and being strongly zero-dimensional.
scientific article; zbMATH DE number 6533977
scientific article