Identities in fixed dimension algebras of multioperations

In algebras of multioperations, unlike algebras of operations, the superassociativity identity does not hold, but only the semi-superassociavity identity is true. For a more detailed study of the identities satisfiable in fixed dimension algebras of multioperations, this work defines the variety to which these algebras belong. In particular, among these identities defining a variety, an identity is introduced that similar to the Dedekind relation for binary relations. From the introduced identities, some consequences are derived that satisfiable in the fixed dimension algebras of multioperations.
Note that the variety is defined in a language whose symbols are interpreted by the superposition metaoperations, the first argument permissibility, and constant projection metaoperations for each argument and the zero multioperation. In this language, the terms are the intersection meta-operations, the permissibility by any argument, the full multioperation, and the inclusion multioperation. Another interesting task is studying quasiidentities satisfiable in the fixed dimension algebras of multioperations.