Year: 2026
Type: preprint
Abstract: We study the Kothe radical (the upper nil radical) in the variety of Novikov algebras. We prove that the class of weakly right nilpotent Novikov algebras coincides with the class of r-nil algebras and forms a radical class. We establish that the Kothe radical is a hereditary radical in the variety of Novikov algebras. Furthermore, we obtain a structural description of the Kothe radical as the intersection of ideals whose corresponding quotient algebras are prime K-semisimple algebras. Finally, we construct an example of a prime r-nil Novikov algebra over a field of characteristic p>0, which implies that the Baer radical is strictly contained in the Kothe radical in this case.
Source: arXiv (Cornell University)
Author: Panasenko, Alexander S.
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Russian Science Foundation
Award: G5942750166
OpenAlex ID: W7224080565