arXiv subjects

Eloise Hamann

Publications and source records attributed to Eloise Hamann.

3 recordsLinked to original sources

arXiv2003

Constants of Differentiation and Differential Ideals

Let R be a differential domain finitely generated over a differential field, F, with field of constants, C, of characteristic 0. Let E be the quotient field of R. The paper investigates necessary and sufficient conditions on R's differential ideals for the constants of differentiation of E to also be C (no new constants). It was known that no proper nonzero differential ideals guarantees no new constants. The paper shows that when C is algebraically closed that if R has only finitely many height one prime differential ideals that E will have no new constants. An example with F infinitely generated over C shows the converse is false. The paper gives conditions on C and F so that when F is finitely generated over C and R is a polynomial ring over F that no new constants in E implies that R has only fintely many height one prime differential ideals.

math.AC↗

arXiv2003

A Counterexample to a Question about Differential Ideals

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.

math.AC↗

arXiv2003

A Question about Differential Ideals

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.

math.AC↗