A Question about Differential Ideals
Abstract
Description
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.
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
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