2003/11/26 by Eloise Hamann, Hamann, Eloise
Mathematics · #13Nxx #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13Nxx
paper · pdf · doi:10.48550/arxiv.math/0311437
This paper has been withdrawn by the author. An intersection of infinitely many prime ideals is not zero as claimed
openalex publication_date 2003/11/26 · arxiv created 2003/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.