Menger hyperalgebras and their representations

Abstract

© 2020 Taylor & Francis Group, LLC. The paper is devoted to the investigation of algebraic hyperstructures. The concept of Menger hyperalgebras, which is a canonical generalization of semihypergroups, is introduced. The emphasis of this paper is on the algebraic nature of such structure concerning subhyperalgebras, homomorphisms and quotient hyperstructures, that allows for a rich algebraic theory. Based on the theory of multiplace functions, multivalued full functions (or hyperoperation) on a general fixed arity is defined. This leads us to construct the Menger hyperalgebras of multivalued full n-ary functions. In particular, we prove that every abstract Menger hyperalgebra can be represented by multivalued full n-ary functions.