Some results on Nilpotency, Solvability and Frattini Theory for Bicommutative, Assosymmetric and Novikov algebras

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 assosymmetric and of Novikov algebras and to introduce a Frattini theory for all of them. A description is also given for semisimple bicommutative algebras over any field.