Abstract
Let K ⊂ R ⊂ P be a tower of fields, N be a P-module, and Δ: R → N be a K-linear differential operator. The aim of this paper is to investigate whether the operator Δ has an extension to P, i.e. if these exists a differential operator Δ′: P → N such that Δ′|R = Δ. The results of this paper were published in Russian in Mat. Zametki 30(2) (1981), 237–248.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bourbaki, N.: Algèbre, livre II, Éléments de mathématique par N. Bourbaki. Premieŕe partie. Les structures fondamentales de l'analyse, Hermann, Paris.
Krasil'shchik, I. S.: Calculus over commutative algebras: a concise user guide, Acta Appl. Math. 49 (1997), 235–248 (this issue).
Krasil'shchik, I. S., Lychagin, V. V., and Vinogradov, A. M.: Geometry of Jet Spaces and Nonlinear Differential Equations, Adv. Stud. Contemp. Math. 1, Gordon and Breach, 1986.
Suzuki, S.: Differentials of commutative rings, Queen's Papers in Pure and Appl. Math. 29, Queen's University Kingston, 1971.
Vinogradov M. M.: Extensions of fields and extensions of linear differential operators, Mat. Zametki 30(2) (1981), 237–248 (in Russian).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vinogradov, M.M. Field Extensions and Extensions of Linear Differential Operators. Acta Applicandae Mathematicae 49, 271–280 (1997). https://doi.org/10.1023/A:1005802708344
Issue Date:
DOI: https://doi.org/10.1023/A:1005802708344