Abstract

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.

抽象的

本文致力于代数超结构的研究。引入了门格高代数的概念，它是半超群的典型概括。本文的重点是关于亚超代数，同态和商超结构的这种结构的代数性质，这提供了丰富的代数理论。基于多位函数的理论，定义了一般固定对数上的多值全函数（或超操作）。这使我们构造了多值全n元函数的Menger超代数。特别地，我们证明了每个抽象的Menger超代数都可以由多值完整n元函数表示。