A Counterexample to a Question about Differential Ideals
| dc.creator | Hamann, Eloise | |
| dc.date | 2003-11-26 | |
| dc.date | 2003-11-30 | |
| dc.date.accessioned | 2026-07-07T05:03:15Z | |
| dc.date.available | 2026-07-07T05:03:15Z | |
| dc.description | This note intended to give a counterexample to a question related to the following theorem. Let D be a differential domain finitely generated over a differential field F with algebraically closed field of constants,C, of characteristic 0. If D has no nonzero proper differential ideals, then the differential constants of the quotient field of D is also C. The converse is known to be false but the question of whether the differential domain D can be finitely extended within its quotient field to a differential domain with no nonzero proper differential ideals has been raised. A counterexample in the case that F is infinitely generated over C has appeared. This paper intended to give a counterexample in the case where F = C negating the natural question whether adding the condition that F be finitely generated over C is sufficient to guarantee a positive answer to the question. The question is still open. | |
| dc.description | This paper has been withdrawn by the author. An intersection of infinitely many prime ideals is not zero as claimed | |
| dc.identifier | https://arxiv.org/abs/math/0311437 | |
| dc.identifier | http://arxiv.org/abs/math/0311437 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69336 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13Nxx | |
| dc.title | A Counterexample to a Question about Differential Ideals | |
| dc.type | text |