From lattices to H v – matrices

In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasiordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv–rings and Hv–matrices and also one recent construction of hyperstructures.