Year: 2026
Type: preprint
Abstract: An algebra is called binary Zinbiel if every subalgebra generated by at most two elements is a Zinbiel algebra. Over a field of characteristic zero, we prove that every finite-dimensional binary Zinbiel algebra is nilpotent. We also show that a subvariety of binary Zinbiel algebras is nil if and only if it does not contain the variety of all Zinbiel algebras. We further prove an analogue of Itô's theorem for binary Zinbiel algebras.
Source: arXiv (Cornell University)
Author: Smadyarov, Nurken
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220471868