Algebraic connections between Menger algebras and Menger hyperalgebras via regularity

Abstract

Menger hyperalgebras of rank n, where n is a fixed integer, can be regarded as a natural generalization of arbitrary semihypergroups. Based on this knowledge, an interesting question arises: what a generalization of regular semihypergroups is. In the article, we establish the notion of v-regular Menger hyperalgebras of rank n, which can be considered as an extension of regular semihypergroups. Furthermore, we study regularity of Menger hyperalgebras of rank n which are induced by some subsets of Menger algebras of rank n. In particular, we obtain sufficient conditions so that the Menger hyperalgebras of rank n are v-regular.