In this paper we consider the class of semihypergroups H such that all sub semihypergroups K⊆H are simple and, when |K|>=3 the fundamental relation β_K is not transitive. For these semihypergroups we prove that hyperproducts of elements in H have size <=2 and the quotient semigroup H/β∗ is trivial. This last result allows us to completely characterize these semihypergroups in terms of a small set of simple semihypergroups of size 3. Finally, we solve a problem on strongly simple semihypergroups introducedin [11].
Fully simple semihypergroups
DE SALVO, Mario;LO FARO, Giovanni
2014-01-01
Abstract
In this paper we consider the class of semihypergroups H such that all sub semihypergroups K⊆H are simple and, when |K|>=3 the fundamental relation β_K is not transitive. For these semihypergroups we prove that hyperproducts of elements in H have size <=2 and the quotient semigroup H/β∗ is trivial. This last result allows us to completely characterize these semihypergroups in terms of a small set of simple semihypergroups of size 3. Finally, we solve a problem on strongly simple semihypergroups introducedin [11].File in questo prodotto:
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