Iterated Antiderivative Extensions
V. Ravi Srinivasan

TL;DR
This paper proves that subfields of iterated antiderivative extensions over a differential field with algebraically closed constants are themselves iterated antiderivative extensions, clarifying their structural properties.
Contribution
It establishes that any differential subfield containing the base field within an iterated antiderivative extension retains the same extension type.
Findings
Subfields of iterated antiderivative extensions are also iterated antiderivative extensions.
The structure of such extensions is preserved under taking differential subfields.
Provides a foundational result for the theory of Liouvillian extensions.
Abstract
Let be a characteristic zero differential field with an algebraically closed field of constants and let be a no new constants extension of . We say that is an \textsl{iterated antiderivative extension} of if is a liouvillian extension of obtained by adjoining antiderivatives alone. In this article, we will show that if is an iterated antiderivative extension of and is a differential subfield of that contains then is an iterated antiderivative extension of .
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Taxonomy
TopicsMatrix Theory and Algorithms
