4-type subvarieties of the variety of associative algebras

Abstract: In this paper, we consider four subvarieties of the variety of associative algebras. We study these subvarieties from the point of view of operads and show connections with well-known algebras such as dendriform algebras and noncommutative Novikov algebras. Finally, we define operations, commutator and anti-commutator on these algebras and obtain some identities under these operations.