Frobenius Differential-Algebraic Universums on Complex Algebraic Curves |
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Authors: | Email author" target="_blank">O?V?GerasimovaEmail author Yu?P?Razmyslov |
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Institution: | 1.Faculty of Mechanics and Mathematics,Moscow State University,Moscow,Russia |
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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 → 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 ∈ 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). |
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