Summary: We look at the interplay between algebraic properties of commutative semi-prime \(f\)-rings vis-a-vis topological properties of the maximal spectra of these rings. We are able to show that, in the case of a strong unit, an \(f\)-ring has the local-global property precisely when its maximal spectrum is zero-dimensional. We also obtain a first-order characterization of this occurrence. We then consider under what conditions we can omit the assumption of a strong unit. These results are then translated to the case where the ring under consideration is \(C(X)\), the ring of continuous real valued functions.
For the entire collection see [Zbl 0778.00030].