Thomas VOUGIOUKLIS
The hyperoperations, called theta-operations (∂), are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define ∂-operations. In this paper, we continue our study on the ∂-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using ∂-operations one obtains, mainly, HV -structures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special HV -rings or HV-fields, so these hyperstructures can be used. Moreover, we study the relation of these ∂-structures with other classes of hyperstructures, especially with the HV-structures.