A Categorical Connection Between Categories $(m, n)$-Hyperrings and $(m, n)$-Ring via the Fundamental Relation $\Gamma^\ast$
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Authors: A. ASADI, R. AMERI AND M. NOROUZI
DOI: 10.46793/KgJMat2103.361A
Abstract:
Let R be an (m,n)-hyperring. The Γ∗-relation on R in the sense of Mirvakili and Davvaz [?] is the smallest strong compatible relation such that the quotient R∕Γ∗ is an (m,n)-ring. We use Γ∗-relation to define a fundamental functor, F from the category of (m,n)-hyperrings to the category of (m,n)-rings. Also, the concept of a fundamental (m,n)-ring is introduced and it is shown that every (m,n)-ring is isomorphic to R∕Γ∗ for a nontrivial (m,n)-hyperring R. Moreover, the notions of partitionable and quotientable are introduced and their mutual relationship is investigated. A functor G from the category of classical (m,n)-rings to the category of (m,n)-hyperrings is defined and a natural transformation between the functors F and G is given.
Keywords:
(m,n)-rings, (m,n)-hyperrings, Γ∗-relation, category.
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