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On Partial Differential Equations in a Field of Prime Characteristic

Published online by Cambridge University Press:  20 November 2018

Arno Jaeger
Arno Jaeger*
Affiliation:
University of Cincinnati
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In classical analysis ordinary differential equations and partial differential equations are distinct concepts, and the transition from one derivation to several partial derivations changes some of their properties distinctly. On the other hand, the algebraic theories of modified ordinary and partial differential equations (5; 6), based on the differentiations in the sense of Hasse (2) and Schmidt (3) and the multidifferentiations in the sense of Jaeger (4), turn out to be strikingly similar in the case of fields of prime number characteristic.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 539 - 542
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Bourbaki, N., Algèbre chap. IV-V, Actualités Scientifiques et Industrielles, no. 1102 (Paris, 1950).Google Scholar
2. Hasse, H., Theorie der höheren Differentiate in einem algebraischen Funktionenkörper mit vollkommenem Konstantenkörper bei beliebiger Charakteristik, J. reine angew. Math., 175 (1936), 50–54.Google Scholar
3. Hasse, H. und Schmidt, F. K., Noch eine Begründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmten, J. reine angew. Math., 177 (1937), 215–237.Google Scholar
4. Jaeger, A., Eine algebraische Theorie vertauschbarer Differentiationen für Körper beliebiger Charakteristik, J. reine angew, Math., 190 (1952), 1–21.Google Scholar
5. Jaeger, A., Gewöhnliche Differentialgleichungen in Körpern von Primzahlcharakteristik, Monatsh. Math., 56 (1952), 181–219.Google Scholar
6. Jaeger, A., Partielle Differentialgleichungen in Körpern von Primzahlcharakteristik, Monatsh. Math., 56 (1952), 265–287.Google Scholar