Iterated antiderivative extensions

作者：Srinivasan V Ravi^*

来源：Journal of Algebra, 2010, 324(8): 2042-2051.

DOI：10.1016/j.jalgebra.2010.03.030

• Differential algebra
• Antiderivatives
• Antiderivative extensions
• Algebraic dependence
• Structure theorem

Let F be a characteristic zero differential field with an algebraically closed field of constants and let E be a no new constants extension of F. We say that E is an iterated antiderivative extension of F if E is a liouvillian extension of F obtained by adjoining antiderivatives alone. In this article, we will show that if E is an iterated antiderivative extension of F and K is a differential subfield of E that contains F then K is an iterated antiderivative extension of F.

• 出版日期2010-10-15