Levi-Civita functional equations on commutative monoids with tractable prime ideals.

Under suitable conditions on the unknown functions, solutions of Levi-Civita functional equations on commutative monoids with no prime ideals are exponential polynomials. This is not generally the case on commutative monoids with prime ideals. Here we describe the solutions of Levi-Civita equations on commutative monoids in which every prime ideal is tractable. Monoids with this property include those which are regular or generated by their squares, as well as many others. Our results also give the continuous solutions on topological commutative monoids with tractable prime ideals. [ABSTRACT FROM AUTHOR]