Algebraic description of rings of continuous functions (Q2784538)

In [Ann. Soc. Sci. Bruxelles, Sér. I 89, 364-368 (1975; Zbl 0304.13021)] \textit{J.-P. Delfosse} announced the result which characterizes the ring \(C(K)\) of all real-valued continuous functions on a compact space \(K\) by six algebraic conditions. In the present paper the authors write: ``Since we have not found any published proof of this result, we have attempted to give an independent proof. However, we have not been able to prove the theorem in Delfosse's formulation. Therefore, in order to prove a characterization theorem of this type, we have had to replace Delfosse's conditions (4)--(6) by our own conditions.'' A detailed sketch of the proof is then given.