Construction of \(n\)-ary \((H,G)\)-hypergroups.
type: Item
instance of: scholarly article
title: Construction of \(n\)-ary \((H,G)\)-hypergroups.
zbMATH Open document ID: 1268.20067
DOI: 10.4171/PM/1917
author: S. M. Anvariyeh
author: Bijan Davvaz
author: S. Mirvakili
published in: Portugaliae Mathematica. Nova Série
publication date: 2013-03-12T00:00:00Z
review text: Let \((H,f)\) be an \(n\)-ary hypergroup and \((G,h)\) be an \(n\)-ary group derived from some binary group. Let \(K\) by the union of a family of non-empty disjoint subsets \(A_g\) of \(H\) uniquely indexed by elements of \(G\) in the way that \(A_e=H\). If the hyper-operation \(f\) is extended to \(K\) in the way that \(f(x_1^n)=A_{h(g_1^n)}\) for all \((x_1^n)\in A_{g_1}\times\cdots\times A_{g_n}\neq H^n\) the structure obtained is an \(n\)-ary hypergroup called an \(n\)-ary \((H,G)\)-hypergroup. Properties and the fundamental relation of such hypergroups are described.
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 20N15
zbMATH DE Number: 6143504
zbMATH Keywords: \(n\)-ary groups
zbMATH Keywords: \(n\)-ary hypergroups
zbMATH Keywords: fundamental relation
zbMATH Keywords: completions
reviewed by: Wiesław A. Dudek
MaRDI profile type: Publication
cites work: Strongly transitive geometric spaces associated to hypermodules.
cites work: On the heart of hypermodules
cites work: Q3094548
cites work: Polygroups derived from cogroups
cites work: Q3137919
cites work: Q4706962
cites work: Binary relations and reduced hypergroups.
cites work: Approximations in \(n\)-ary algebraic systems
cites work: NEUTRAL ELEMENTS, FUNDAMENTAL RELATIONS AND n-ARY HYPERSEMIGROUPS
cites work: On the \(\gamma_n^*\)-complete hypergroups.
cites work: Q3575415
cites work: Q3734736
description: scientific article; zbMATH DE number 6143504