Concerning maximal \(\ell\)-ideals of rings of continuous integer-valued functions. (Q485108)

From the author's summary: Maximal \(\ell\)-ideals of the ring \(C(X,\mathbb Z)\) of continuous integer-valued functions on a topological space \(X\) were characterized by Subramanian to be exactly the minimal prime ideals of this ring. This note supplements this result by showing that, in fact, these ideals are also exactly the maximal \(z\)-ideals, exactly the maximal \(d\)-ideals, and exactly the maximal pure ideals of this ring. [\dots] we show that what has just been said holds in any ring of continuous integer-valued functions on a zero-dimensional frame.