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Convolutions on WASS hyperstructures. (English) Zbl 0889.20046

Several convolutions in hypergroups or in more general hyperstructures are defined. If \(G\) is a finite weakly associative hypergroupoid and \(K\) is a field, a convolution \(*\), as hyperproduct, is defined on the algebra \(K[G]\). Properties of this hyperproduct are studied and examples on special classes of hyperstructures are investigated.

MSC:

20N20 Hypergroups
16Y99 Generalizations
16S34 Group rings
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References:

[1] Corsini, P., Prolegomena of Hypergroup Theory (1993), Aviani Editore · Zbl 0785.20032
[2] Vougiouklis, Th., Representations of hypergroups, Hypergroup algebra, (Convegno: Ipergruppi, str. mult. appl. Udine (1985)), 59-73
[3] Vougiouklis, Th., The fundamental relation in hyperrings, The general hyperfield, (Proc. 4th Internat. Congr. AHA. Proc. 4th Internat. Congr. AHA, Xanthi 1990 (1991), World Scientific: World Scientific Singapore), 209-217
[4] Th. Vougiouklis, The very thin hypergroups and the \(S\); Th. Vougiouklis, The very thin hypergroups and the \(S\) · Zbl 0945.20524
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