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The problem of the Hv-representations of Hv-groups by Hv-matrices, is presented. Classes of Hv-rings useful in the theory of representations are introduced. The advantages of some classes of the Hv-matrices in the representation theory is pointed out. c © 1999 Elsevier Science B.V. All rights reserved.
If a hyperoperation is weak associative then every greater hyperoperation, defined on the same set, is also weak associative. Using this property, the set of all Hv-groups with a scalar unit, defined on a set with three elements is determined.
Soft set theory, introduced by Molodtsov, has been considered as an effective mathematical tool for modeling uncertainties. In this paper, we apply fuzzy soft sets to Γ-hypermodules. The concept of (∈γ ,∈γ ∨ qδ)-fuzzy soft Γ-subhypermodules of Γ-hypermodules is first introduced. Some new characterizations are investigated. In particular, a kind of new… (More)
The quiver of hyperstructures, especially very large classes of them, can be used in new scientific theories such as Ying’s twin universes. We present the largest class of hyperstructures which can be used as a model to represent the twin universe cosmos as even more new axioms or conditions are considered.
Hyperstructure theory was born in 1934 when Marty  defined hypergroups as a generalization of groups. Let H be a non-empty set and let ℘∗(H) be the set of all non-empty subsets of H. A hyperoperation on H is a map ◦ : H ×H −→ ℘∗(H) and the couple (H, ◦) is called a hypergroupoid. If A and B are non-empty subsets of H, then we denote A◦B = ∪ a∈A, b∈B… (More)
We present a hyperproduct on non square matrices by using a generalization of the well known P-hopes. This theory is connected with the corresponding classical algebra, mainly with the theory of representations by (hyper) matrices. This can be achieved by using the fundamental relations defined on the hyperstructures.