Mathematics – Commutative Algebra
Scientific paper
2003-11-26
Mathematics
Commutative Algebra
This paper has been withdrawn by the author. An intersection of infinitely many prime ideals is not zero as claimed
Scientific paper
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.
No associations
LandOfFree
A Counterexample to a Question about Differential Ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Counterexample to a Question about Differential Ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Counterexample to a Question about Differential Ideals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-122492