Frobenius Differential-Algebraic Universums on Complex Algebraic Curves

In terms of differential generators and differential relations for a finitely generated commutative- associative differential C-algebra A (with a unit element) we study and determine necessary and sufficient conditions for the fact that under any Taylor homomorphism \(\widetilde \psi \)M: A → Cz]] the transcendence degree of the image \(\widetilde \psi \)M(A) over C does not exceed 1 \(\left( {\widetilde \psi M{{\left( a \right)}^{\underline{\underline {def}} }}\sum\limits_{m = 0}^\infty {\psi M\left( {{a^{\left( m \right)}}} \right)} } \right)\frac{{{z^m}}}{{m!}}\), where a ∈ A, M ∈ Spec_CA is a maximal ideal in A, a^(m) is the result of m-fold application of the signature derivation of the element a, and ψM is the canonic epimorphism A → A/M).