Nonstandard methods for bounds in differential polynomial rings

JOURNAL OF ALGEBRA

卷:360

Article

Harrison-Trainor, Matthew¹  Klys, Jack¹  Moosa, Rahim¹ 

[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

关键词: Differential algebra;    Characteristic sets;    Ultraproducts;    Internal differential polynomials;   

DOI  :  10.1016/j.jalgebra.2012.03.013

来源: Elsevier

【 摘 要 】

Motivated by the problem of the existence of bounds on degrees and orders in checking primality of radical (partial) differential ideals, the nonstandard methods of van den Dries and Schmidt [L.. van den Dries, K. Schmidt, Bounds in the theory of polynomial rings over fields. A nonstandard approach, Invent. Math. 76 (1984) 77-91] are here extended to differential polynomial rings over differential fields. Among the standard consequences of this work are: a partial answer to the primality problem, the equivalence of this problem with several others related to the Ritt problem, and the existence of bounds for characteristic sets of minimal prime differential ideals and for the differential Nullstellensatz. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free