2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70169Let $A$ be a finite-dimensional local commutative algebra over $R$, $\dim_RA=n$. In this work we consider compact manifolds over $A$, and prove that the real part of an $A$-differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.Differential GeometryComplex Variables53C10; 53C12; 53C15text