Algorithmic problems for differential polynomial algebras

@article{Umirbaev2015AlgorithmicPF,
  title={Algorithmic problems for differential polynomial algebras},
  author={U. Umirbaev},
  journal={arXiv: Rings and Algebras},
  year={2015}
}
  • U. Umirbaev
  • Published 2015
  • Mathematics
  • arXiv: Rings and 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. 

References

SHOWING 1-10 OF 41 REFERENCES
Membership problem for differential ideals generated by a composition of polynomials
Differential Gröbner bases in one variable and in the partial case
Occurrence problem for free solvable groups
Gröbner–Shirshov bases and their calculation
A FINITELY PRESENTED SOLVABLE GROUP WITH UNSOLVABLE WORD PROBLEM
Standard Bases of Differential Ideals
Subalgebras of Free Lie Algebras
Differential and Difference Dimension Polynomials
Galois Theory of Linear Differential Equations
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