SOME BASIC THEOREMS IN DIFFERENTIAL ALGEBRA (CHARACTERISTIC p, ARBITRARY)

Keywords

Mathematics, Ring (chemistry), Differential algebra, Differential (mechanical device), Integral domain

References

• Foundations of Algebraic GeometryAndré Weil — 1946
• Modular fields. I. Separating transcendence basesSaunders Mac Lane — 1939
• Some properties of ideals in rings of power seriesClaude Chevalley — 1944
• On the basis theorem for differential systemsE. R. Kolchin — 1942
• Extensions of Differential Fields, IIE. R. Kolchin — 1942
• Differential Fields and Ideals of Differential FormsH. W. Raudenbush — 1933
• Some Properties of Ideals in Rings of Power SeriesClaude Chevalley — 1944
• Differential AlgebraJ. Ritt — 1950
• On the Basis Theorem for Differential SystemsE. R. Kolchin — 1942

Cited by

• Differential flatness and defect: an overviewMichel Fliess, Jean Lévine, Philippe Martin — 1995
• Model theory of fieldsDavid Marker, Margit Messmer, Anand Pillay — 1996
• An optimization of Seidenberg's elimination algorithm in differential algebraFrançois Boulier — 1996
• The model theory of ordered differential fieldsMichael F. Singer — 1978
• The model theory of differential fields revisitedCarol Wood — 1976
• Probabilistic algorithms for computing resolvent representations of regular differential idealsThomas Cluzeau, Évelyne Hubert — 2008
• Approximation for Frobenius algebraic equations in Witt vectorsLuc Bélair — 2009
• Abstract differential algebra and the analytic case. IIA. Seidenberg — 1958
• Resolvent Representation for Regular Differential IdealsThomas Cluzeau, Évelyne Hubert — 2003
• A SINGLE SENSOR SELECTION THEOREM FOR RATIONAL STATE SYSTEMSSette Diop — 2006
• Filtrations in feedback synthesis: Part I – Systems and feedbacksEmmanuel Delaleau, Paulo Sérgio Pereira da Silva — 1998
• Infinitary Model-Theoretic Properties Of χ-Saturated StructuresVolker Weispfenning — 1973
• Representation for the radical of a finitely generated differential idealFrançois Boulier, Daniel Lazard, François Ollivier — 1995
• Computing representations for radicals of finitely generated differential idealsFrançois Boulier, Daniel Lazard, François Ollivier — 2009
• Flatness and defect of non-linear systems: introductory theory and examplesMichel Fliess, Jean Lévine, Philippe Martin — 1995
• The primitive element theorem for differential fields with zero derivation on the ground fieldGleb Pogudin — 2014
• Specializations in differential algebraAzriel Rosenfeld — 1959
• On separating transcendency bases for differential fieldsA. Seidenberg — 1955
• FIELDS WITH SEVERAL COMMUTING DERIVATIONSDavid A. Pierce — 2007
• On the complexity of the resolvent representation of some prime differential idealsLisi D’Alfonso, Gabriela Jeronimo, Pablo Solernó — 2006

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