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- Title
On intra-regular ordered hypersemigroups.
- Authors
Kehayopulu, Niovi
- Abstract
We present a structure theorem referring to the decomposition of ordered hypersemigroups into simple components. For an intra-regular ordered hypersemigroup H, the very simple form of its principal filters leads to a characterization of H as a semilattice of simple hypersemigroups; that is as an ordered hypersemigroup for which there exists a semilattice congruence σ such that (x)σ is a simple subhypersemigroup of H for every x ∈ H. This is equivalent to saying that H is a union of simple subhypersemigroups of H. In addition, an ordered hypersemigroup 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.
- Subjects
SEMIGROUPS (Algebra); SEMILATTICES; CONGRUENCE lattices; BINARY operations; QUASIGROUPS
- Publication
Quasigroups & Related Systems, 2018, Vol 26, Issue 2, p239
- ISSN
1561-2848
- Publication type
Article