| Abstract: | 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 → C[[z]] 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}} }}sumlimits_{m = 0}^infty {psi Mleft( {{a^{left( m right)}}} right)} } right)frac{{{z^m}}}{{m!}}), where a ∈ A, M ∈ SpecCA 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). |
