Among hyperstructures of type U on the right having small size, the order 6 is a relevant case. Indeed, only if the order is >= 6 there exist proper semihypergrops and hypergroups of type U on the right whose right scalar identity is not also left identity. In the present paper we show a construction of hypergroups of type U on the right whose right scalar identity is not also left identity. That construction characterizes completely the case of order 6, and allows to introduce a semi-ordering structure within that case. With the help of that semi-ordering, and of symbolic computation software, we show that these hypergroups can be obtained as hyperproduct extensions of 41 minimal hypergroups, and that the number of their isomorphism classes is 946.
Hypergroups with a Strongly Unilateral Identity
DE SALVO, Mario;LO FARO, Giovanni
2013-01-01
Abstract
Among hyperstructures of type U on the right having small size, the order 6 is a relevant case. Indeed, only if the order is >= 6 there exist proper semihypergrops and hypergroups of type U on the right whose right scalar identity is not also left identity. In the present paper we show a construction of hypergroups of type U on the right whose right scalar identity is not also left identity. That construction characterizes completely the case of order 6, and allows to introduce a semi-ordering structure within that case. With the help of that semi-ordering, and of symbolic computation software, we show that these hypergroups can be obtained as hyperproduct extensions of 41 minimal hypergroups, and that the number of their isomorphism classes is 946.Pubblicazioni consigliate
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