A Question about Differential Ideals
Abstract
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.
Cite
@article{arxiv.math/0311006,
title = {A Question about Differential Ideals},
author = {Eloise Hamann},
journal= {arXiv preprint arXiv:math/0311006},
year = {2007}
}
Comments
10 pages. Latex This paper is an extract of a paper about to appear in Comms. in Algebra. The paper's 2nd. counterexample has a fatal flaw that was discovered too late to pull the paper. This posting is to alert readers