In this paper, we consider four types of subvarieties of the variety of associative algebras. We show their connections with well-known classes of algebras, such as dendriform algebras and noncommutative Novikov algebras. Finally, we define the commutator and anti-commutator operations on these algebras and derive several identities satisfied by these operations.
Kunanbayev et al. (Thu,) studied this question.