In this paper we give an
example of a Wallman ring 𝒜 on a topological space X such that the associated
compactification ω(X,Z(𝒜)) is disconnected and 𝒜 is not a direct sum of any two
proper ideals, herewith solving a question raised by H. L. Bentley and B. J. Taylor.
Also, an example of a uniformly closed Wallman ring which is not a sublattice is
given.