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Title: Hilbert-Type Dimension Polynomials of Intermediate Difference-Differential Field Extensions
Let K be an inversive difference-differential field and L a (not necessarily inversive) finitely generated difference-differential field extension of K. We consider the natural filtration of the extension L/K associated with a finite system \eta of its difference-differential generators and prove that for any intermediate difference-differential field F, the transcendence degrees of the components of the induced filtration of F are expressed by a certain numerical polynomial \chi_{K, F,\eta}(t). This polynomial is closely connected with the dimension Hilbert-type polynomial of a submodule of the module of K\"ahler differentials $\Omega_{L^{\ast}|K} where L^{\ast} is the inversive closure of L. We prove some properties of polynomials \chi_{K, F,\eta}(t) and use them for the study of the Krull-type dimension of the extension L/K. In the last part of the paper, we present a generalization of the obtained results to multidimensional filtrations of L/K associated with partitions of the sets of basic derivations and translations.  more » « less
Award ID(s):
1714425
PAR ID:
10301698
Author(s) / Creator(s):
Date Published:
Journal Name:
Lecture notes in computer science
Volume:
11989
ISSN:
0302-9743
Page Range / eLocation ID:
64 - 79
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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