Geodesic
A Categorical Connection Between Categories $(m,n)$-Hyperrings and $(m,n)$-Ring via the Fundamental Relation $\Gamma^*$
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 361 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $R$ be an $(m,n)$-hyperring. The $\Gamma^\ast$-relation on $R$ in the sense of Mirvakili and Davvaz \cite{[26]} is the smallest strong compatible relation such that the quotient $R/\Gamma^\ast$ is an $(m,n)$-ring. We use $\Gamma^\ast$-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 $R/\Gamma^\ast$ 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.
Classification : 20N20 20N15, 18D35
Keywords: $(m;n)$-rings, $(m;n)$-hyperrings, $\Gamma^\ast$-relation, category 
@article{KJM_2021_45_3_a3,
     author = {Ameneh Asadi and Reza Ameri and Morteza Norouzi},
     title = {A {Categorical} {Connection} {Between} {Categories} $(m,n)${-Hyperrings} and $(m,n)${-Ring} via the {Fundamental} {Relation} $\Gamma^*$},
     journal = {Kragujevac Journal of Mathematics},
     pages = {361 },
     year = {2021},
     volume = {45},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a3/}
}
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Ameneh Asadi; Reza Ameri; Morteza Norouzi. A Categorical Connection Between Categories $(m,n)$-Hyperrings and $(m,n)$-Ring via the Fundamental Relation $\Gamma^*$. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 361 . http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a3/