A Question about Differential Ideals

Details A Question about Differential Ideals A Question about Differential Ideals

2003-11-02

arxiv.org/abs/math/0311006v1

Mathematics

Commutative Algebra

10 pages. Latex This paper is an extract of a paper about to appear in Comms. in Algebra. The paper's 2nd. counterexample has

Scientific paper

The paper investigates the converse to the following theorem. Let R be a differential domain R which is finitely generated over a differential field F whose field of constants is algebraically closed of characteristic 0. If R has no proper nonzero differential ideals, then the quotient field, E, of R has no new constants. The converse is false, but a question was raised about the existence of a finitely generated extension of R within E which has no proper nonzero differential ideals when E has no new constants. This posted paper gives one example to show this is false and two limited positive results in Krull dimension one or two.

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