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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 ∨ q δ)-fuzzy soft Γ-subhypermodules of Γ-hypermodules is first introduced. Some new characterizations are investigated. In particular, a kind of new… (More)
The H v-structures are hyperstructures where the equality is replaced by the non-empty intersection. The fact that this class of the hyperstructures is very large, one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory. In the present paper we introduce a kind of hyperoperations which… (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.
The class of (m, n)-ary Hv-modules is larger than the well known class Hv-modules. A wide subclass of (m, n)-ary Hv-modules is n-ary P-Hv-modules. In this paper, we consider and study a module over a ring and we define three kinds of external n-ary P-hyperoperations. By using external n-ary P-hyperoperations and certain conditions, we construct several (m,… (More)
First introduced and studied: (The term hope=hyperoperation (2008)) P-hypergroups, single-power cyclicity (1981). Fundamental relations in hyper-rings (γ*-relation) and Representations of hypergroups by generalized permutations and hypermatrices (1985). Very Thin hyperstructures, S-construction (1988). Uniting elements procedure (1989), with P.Corsini.… (More)