On Certain Towers of Extensions by Antiderivatives

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dc.contributor.advisorMagid, Andy R
dc.creatorSrinivasan, Varadharaj Ravi
dc.date.accessioned2019-06-03T20:36:13Z
dc.date.available2019-06-03T20:36:13Z
dc.date.issued2009
dc.description.abstractLet F be a characteristic zero
dc.description.abstractdifferential field with an algebraically closed field of constants
dc.description.abstractC . Let E and K be no new constants extensions of F, E contains K, Kis an extension by antiderivatives of F
dc.description.abstractand Econtain antiderivatives y1,&hellip,yn of K. The
dc.description.abstractantiderivatives y1,&hellip,ynof K are called J-I-E
dc.description.abstractantiderivatives if the derivative of each yisatisfies certain conditions. We will provide a new proof for the Kolchin-Ostrowski theorem and
dc.description.abstractgeneralize this theorem for a tower of extensions by J-I-E
dc.description.abstractantiderivatives and use this generalized version of the theorem to
dc.description.abstractclassify the finitely differentially generated subfields of this
dc.description.abstracttower. In the process, we will show that the J-I-E antiderivatives
dc.description.abstractare algebraically independent over the ground differential field.
dc.description.abstractAn example of a J-I-E tower is the iterated antiderivative extensions
dc.description.abstractof the field of rational functions C(x) generated by iterated
dc.description.abstractlogarithms, closed at each stage by all (translation)
dc.description.abstractautomorphisms. We analyze the algebraic and differential structure
dc.description.abstractof these extensions. In particular, we show that the nth iterated
dc.description.abstractlogarithms and their translates are algebraically independent over
dc.description.abstractthe field generated by all lower level iterated logarithms. Our
dc.description.abstractanalysis provides an algorithm for determining the differential
dc.description.abstractfield generated by any rational expression in iterated logarithms.
dc.format.extent98 pages
dc.format.mediumapplication.pdf
dc.identifier99327594402042
dc.identifier.urihttps://hdl.handle.net/11244/320235
dc.languageen_US
dc.relation.requiresAdobe Acrobat Reader
dc.subjectDifferential algebra
dc.subjectDifferential calculus
dc.thesis.degreePh.D.
dc.titleOn Certain Towers of Extensions by Antiderivatives
dc.typetext
dc.typedocument
ou.groupCollege of Arts and Sciences::Department of Mathematics

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