We never work on ordered hypersemigroups directly.
📌 3 Key Takeaways
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Objective & Hypothesis:It has been shown in Turk J Math 2019; 43 (5): 2592–2601 that many results on hypersemigroups can be obtained directly as corollaries of more general results from the theory of lattice ordered semigroups, ∨e-semigroups or poe-semigroups.
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Key Findings & Data:The present note shows that although this is not exactly the case for ordered hypersemigroups, even in this case various results may be suggested from analogous results for le, ∨e or poesemigroups and direct proofs derive along the lines of those le, ∨e or poe-semigroups setting as well; the sets in the investigation provides a further indication that the results on this structure come from the lattice ordered semigroups or ordered semigroups in general.
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Conclusion & Impact:We never work on ordered hypersemigroups directly.
🔬Design:Research Article
📍Scope:2019 Verileri
⚙️Variables:Domain Parameters
Abstract
It has been shown in Turk J Math 2019; 43 (5): 2592–2601 that many results on hypersemigroups can be obtained directly as corollaries of more general results from the theory of lattice ordered semigroups, ∨e-semigroups or poe-semigroups. The present note shows that although this is not exactly the case for ordered hypersemigroups, even in this case various results may be suggested from analogous results for le, ∨e or poesemigroups and direct proofs derive along the lines of those le, ∨e or poe-semigroups setting as well; the sets in the investigation provides a further indication that the results on this structure come from the lattice ordered semigroups or ordered semigroups in general. In many cases, whenever we have a look at any result on lattice ordered semigroups, we immediately know if can be transferred to ordered hypersemigroups. We never work on ordered hypersemigroups directly.
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Cite This Article
KEHAYOPULU, N. (2022). Relationship between lattice ordered semigroups and ordered hypersemigroups. Turkish Journal of Mathematics, Cilt: 45 - Sayı: 4, 1724–1737. https://ajindex.com/articles/607391
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