Hyperrings and -relations. A general approach.

Abstract: The study of the equivalence relations of particular multialgebras for which the factor multialgebras are universal algebras satisfying certain identities is a very important and intensively studied topic in multialgebra theory and not only. Our paper provides a general multialgebraic approach for the construction of all these relations and also some important and interesting properties concerning the construction of the corresponding factor universal algebra. One of the purposes of our approach is to improve some results concerning -relations of hyperrings and Krasner hyperrings and we will do this in the last sections of this paper. [Copyright &y& Elsevier]