Geodesic
Vector Valued Hyperstructures
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 259

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Vector valued hyperstructures, i.e., $(n,m)$-hyperstructures, where $n=m+k$, $k\geq 1$, as a generalization of vector valued structures and $n$-ary hyperstructures are introduced and supported by many examples. We have presented some initial properties about $(n,m)$-hypersemigroups and $(n,m)$-hypergroups. Moreover, by properly defining regular and strongly regular binary relations, from vector valued hypersemigroups (hypergroups) we obtain "ordinary" vector valued semigroups (groups) on quotients.
Classification : 20M10 20N99, 20N20
Keywords: $(n;m)$-hyperoperation, $(n;m)$-hypergroupoid, $(n;m)$-hypersemi\-group, $(n;m)$-hyperquasigroup, $(n;m)$-hypergroup, regular relation, strongly regular relation 
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     author = {V. Miovska and V. Celakoska-Jordanova and B. Davvaz},
     title = {Vector {Valued} {Hyperstructures}},
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V. Miovska; V. Celakoska-Jordanova; B. Davvaz. Vector Valued Hyperstructures. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 259 . http://geodesic.mathdoc.fr/item/KJM_2018_42_2_a8/