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

Towers, David (2025) Nilpotency, Solvability and Frattini Theory for Bicommutative, Assosymmetric and Novikov algebras. Communications in Algebra, 53 (3). pp. 917-928. ISSN 0092-7872

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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.