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<cfTitle cfLangCode='EN' cfTrans='o'>On intra-regular ordered hypersemigroups</cfTitle>
<cfKeyw cfLangCode='EN' cfTrans='o'>Ordered hypersemigroup; semilattice (complete semilattice) congruence; intra-regular; semilattice of simple hypersemigroups; prime; simple.</cfKeyw>
<cfAbstr cfLangCode='EN' cfTrans='o'><p>We present a structure theorem referring to the decomposition of ordered hypersemi- groups into simple components. For an intra-regular ordered hypersemigroup H, the very simple form of its principal lters leads to a characterization of H as a semilattice of simple hypersemi- groups; that is as an ordered hypersemigroup for which there exists a semilattice congruence  such that (x) is a simple subhypersemigroup of H for every x 2 H. This is equivalent to saying that H is a union of simple subhypersemigroups of H. In addition, an ordered hyper- semigroup H is intra-regular and the hyperideals of H form a chain if and only if it is a chain of simple hypersemigroups. On this occasion, some further results related to intra-regular ordered hypersemigroups have been also given.</p></cfAbstr>
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