P-compatible identities are built up from terms with a special structure. We investigate a variety defined by a set ofP-compatible hybrid identities and answer the question whether a variety defined by a set ofP-compatible hyperidentities can be solid.

We construct a class K of algebras which are matrices of the logical system Z introduced in [4]. It is shown that algebras belonging to the class K are decomposable into disjoint subalgebras which are Boolean algebras.