Frobenius Differential-Algebraic Universums on Complex Algebraic Curves / O. V. Gerasimova and Yu. P. Razmyslov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2018. ¹ 4. P. 3-9 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 131-136].

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 \to \mathbb{C}[[z]] the transcendence degree of the image \widetilde{\psi }_M(A) over C does not exceed 1 (\widetilde{\psi }_M (a) \stackrel{{\rm def}}{=} \sum \limits_{m=0}^{\infty } \psi_M(a^{(m)}) \frac{z^m}{m!}, where a \in A, M \in{\rm Spec}_{\mathbb{C}} A is a maximal ideal in A, a^{(m)} is the result of m-fold application of the signature derivation of the element a, and \psi_M is the canonic epimorphism A \to A/M).

Key words: differential algebra, its rank, Taylor homomorphism, analytic spectrum, trajectory germ, orbit closure, affine algebraic curve.