The primitive element theorem for differential fields with zero derivation on the ground field

Gleb A. Pogudin

doi:10.1016/j.jpaa.2015.02.004

The primitive element theorem for differential fields with zero derivation on the ground field

Gleb A. Pogudin

Moscow State University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we strengthen Kolchin's theorem [1] in the ordinary case. It states that if a differential field E is finitely generated over a differential subfield F⊂E, trdeg_FE<∞, and F contains a nonconstant, i.e., an element f such that f^'≠0, then there exists a∈E such that E is generated by a and F. We replace the last condition with the existence of a nonconstant element in E.

Original language	English
Pages (from-to)	4035-4041
Number of pages	7
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2015.02.004
Publication status	Published - 1 Sept 2015
Externally published	Yes

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title = "The primitive element theorem for differential fields with zero derivation on the ground field",

abstract = "In this paper we strengthen Kolchin's theorem [1] in the ordinary case. It states that if a differential field E is finitely generated over a differential subfield F⊂E, trdegFE<∞, and F contains a nonconstant, i.e., an element f such that f'≠0, then there exists a∈E such that E is generated by a and F. We replace the last condition with the existence of a nonconstant element in E.",

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N2 - In this paper we strengthen Kolchin's theorem [1] in the ordinary case. It states that if a differential field E is finitely generated over a differential subfield F⊂E, trdegFE<∞, and F contains a nonconstant, i.e., an element f such that f'≠0, then there exists a∈E such that E is generated by a and F. We replace the last condition with the existence of a nonconstant element in E.

AB - In this paper we strengthen Kolchin's theorem [1] in the ordinary case. It states that if a differential field E is finitely generated over a differential subfield F⊂E, trdegFE<∞, and F contains a nonconstant, i.e., an element f such that f'≠0, then there exists a∈E such that E is generated by a and F. We replace the last condition with the existence of a nonconstant element in E.

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JF - Journal of Pure and Applied Algebra

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The primitive element theorem for differential fields with zero derivation on the ground field

Abstract

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