Algorithmic problems for differential polynomial algebras

DOI10.1016/j.jalgebra.2016.02.010zbMath1371.12005arXiv1509.07230OpenAlexW2963478822MaRDI QIDQ267385

Ualbei Utmakhanbetovich Umirbaev

Publication date: 8 April 2016

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.07230

zbMATH Keywords

Groebner basesdifferential polynomial algebrasMinsky machinesthe ideal membership problemthe subalgebra membership problem

Mathematics Subject Classification ID

Decidability and field theory (12L05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Differential graded algebras and applications (associative algebraic aspects) (16E45) Differential algebra (12H05) Computational aspects of associative rings (general theory) (16Z05)

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Cites Work

• Die Unterringe der freien Lieschen Ringe
• The word problem for subvarieties of the variety \({\mathfrak N}_ 2{\mathfrak A}\)
• The occurrence problem for extensions of Abelian groups by nilpotent groups
• Systems of linear equations and the word problem for the varieties \({\mathfrak N}_2{\mathfrak N}_c\) of Lie algebras
• The occurrence problem for Lie algebras
• Algorithmic problems in associative algebras
• Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence
• Occurrence problem for free solvable groups
• Membership problem for differential ideals generated by a composition of polynomials
• Associative differential operations
• Systems of linear equations over associative algebras and the occurrence problem for lie algebras
• ALGORITHMIC PROBLEMS IN VARIETIES
• The occurrence problem for free metanilpotent Lie algebras
• Gröbner–Shirshov bases and their calculation
• Ideals, Varieties, and Algorithms
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