Zinbiel algebras are nilpotent
David A. Towers
TL;DR
This paper proves that all finite-dimensional Zinbiel algebras over any field are nilpotent, extending earlier results that they are only known to be solvable.
Contribution
It establishes the nilpotency of finite-dimensional Zinbiel algebras, a stronger structural property than previously known.
Findings
All finite-dimensional Zinbiel algebras are nilpotent.
Extension of solvability results to nilpotency.
Applicable over arbitrary fields.
Abstract
In this paper we show that every finite-dimensional Zinbiel algebra over an arbitrary field is nilpotent, extending a previous result by other authors that they are solvable.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras