Which are the Maximal Ideals ?

Ideals of continuous functions which satisfy an off diagonality condition proved to be important connected with the solution of large classes of nonlinear PDEs, and more recently, in General Relativity and Quantum Gravity. Maximal ideals within those which satisfy that off diagonality condition are important since they lead to differential algebras of generalized functions which can handle the largest classes of singularities. The problem of finding such maximal ideals satisfying the off diagonality condition is formulated within some background detail, and commented upon.