Algorithmic problems for differential polynomial algebras

We prove that the ideal membership problem and the subalgebra membership problem are algorithmically undecidable for differential polynomial algebras with at least two basic derivation operators.

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Bibliographic Details
Published in:Journal of algebra 2016-06, Vol.455, p.77-92
Main Author: Umirbaev, Ualbai
Format: Article
Language:English
Subjects:
Differential polynomial algebras
Gröbner bases
Minsky machines
The ideal membership problem
The subalgebra membership problem
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Description
Summary:We prove that the ideal membership problem and the subalgebra membership problem are algorithmically undecidable for differential polynomial algebras with at least two basic derivation operators.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2016.02.010