Constructing a new class of $H_v$-semigroups

Document Type : Research Articles

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Department of science, Mahallat institute of higher education

Abstract

Let X be a non-empty set and H_X be the set of all mappings from
X to P^*(X), when P^*(X) is the family of all non-empty subsets of
X. In this paper, we de fine the hyperoperation \circledcirc on H_X such that
(H_X;\circledcirc) is an Hv-semigroup. Then we prove that the fundamental
relation \beta on H_X is the trivial relation.

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