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SM ISO690:2012 KEHAYOPULU, Niovi. A note on hyperideals in ordered hypersemigroups. In: Quasigroups and Related Systems, 2018, vol. 26, nr. 1(39), pp. 79-85. ISSN 1561-2848. |
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Quasigroups and Related Systems | |||||
Volumul 26, Numărul 1(39) / 2018 / ISSN 1561-2848 | |||||
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CZU: 512.534 | |||||
MSC 2010: 06F99. | |||||
Pag. 79-85 | |||||
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Rezumat | |||||
Abstract. For an ordered hypersemigroup H, we denote by Nthe semilattice congruence on H defined by xNy if and only if the hyperfilters of H generated by the elements x and y coincide. We first prove that this is a complete semilattice congruence on H. Moreover, if H is an ordered hypersemigroup, T a hyperfilter of H and, for a class (z)N of H there is an element in the intersection T \ (z)N, then the class (z)N is a subset of T. From these two statements, the following two important results can be obtained: (1) If H is an ordered hypersemigroup, then each hyperideal of some (z)N-class of H does not contain proper hyperfilters. As a consequence, (2) every prime hyperideal of an ordered hypersemigroup is decomposable into its N-classes |
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Cuvinte-cheie Orderedhyp ersemigroup, completesemilatticecongruence, hyp erlter, hyp erideal, primehyp eridea |
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