On radicals of Novikov algebras
A. S. Panasenko

TL;DR
This paper investigates the structure of radicals in Novikov algebras, establishing key properties of ideals and radicals, and clarifying their behavior in finite-dimensional cases over various fields.
Contribution
It provides new insights into the radicals of Novikov algebras, including their coincidence and non-existence results in finite dimensions over specific fields.
Findings
Nonzero ideals in prime Novikov algebras are non-associative.
Baer and Andrunakievich radicals coincide in finite-dimensional Novikov algebras over certain fields.
Right quasiregular radical does not exist in finite-dimensional Novikov algebras.
Abstract
We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and left quasiregular radical coincide in finite dimensional Novikov algebras over a field of characteristic 0 or algebraically closed field of odd characteristic. We show non-existence of right quasiregular radical in finite dimensional Novikov algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras
