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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 },
     publisher = {mathdoc},
     volume = {45},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a3/}
}
TY  - JOUR
AU  - Ameneh Asadi
AU  - Reza Ameri
AU  - Morteza Norouzi
TI  - A Categorical Connection Between Categories $(m,n)$-Hyperrings and $(m,n)$-Ring via the Fundamental Relation $\Gamma^*$
JO  - Kragujevac Journal of Mathematics
PY  - 2021
SP  - 361 
VL  - 45
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a3/
LA  - en
ID  - KJM_2021_45_3_a3
ER  - 
%0 Journal Article
%A Ameneh Asadi
%A Reza Ameri
%A Morteza Norouzi
%T A Categorical Connection Between Categories $(m,n)$-Hyperrings and $(m,n)$-Ring via the Fundamental Relation $\Gamma^*$
%J Kragujevac Journal of Mathematics
%D 2021
%P 361 
%V 45
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a3/
%G en
%F KJM_2021_45_3_a3
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/