Locally Nilpotent Derivations of Free Algebra of Rank Two

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• ISSN: 1815-0659
• Main Authors: Drensky, V., Makar-Limanov, L.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210297
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Locally Nilpotent Derivations of Free Algebra of Rank Two / V. Drensky, L. Makar-Limanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 31 назв. — англ.

In commutative algebra, if δ is a locally nilpotent derivation of the polynomial algebra [x₁, …, xd] over a field of characteristic 0 and w is a nonzero element of the kernel of δ, then Δ=wδ is also a locally nilpotent derivation with the same kernel as δ. In this paper, we prove that the locally n...