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Nilpotency, Solvability and Frattini Theory for Bicommutative, Assosymmetric and Novikov algebras

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Published
<mark>Journal publication date</mark>31/03/2025
<mark>Journal</mark>Communications in Algebra
Issue number3
Volume53
Number of pages12
Pages (from-to)917-928
Publication StatusPublished
Early online date5/09/24
<mark>Original language</mark>English

Abstract

This paper starts by showing that, for algebras in a certain class, the
concepts of weak nilpotency and nilpotency coincide. It goes on to describe
some solvability and nilpotency properties of bicommutative algebras, of as-
sosymmetric algebras and of Novikov algebras and to introduce a Frattini
theory for all of them. A description is also given for semisimple bicommu-
tative algebras over any field.