To the question about the maximum principle for manifolds over local algebras

We consider manifolds over a local algebra $A$. We study basis functions of the canonical foliation which represent the real parts of $A$-differentiable functions. We prove that these are constant functions. We find the form of $A$-differentiable functions on some manifolds over local algebras, in particular, on compact manifolds. We obtain an estimate for the dimension of some spaces of 1-forms and analogs of the above results for the projective mappings of foliations.