In this paper, the notion of weak hyperfilters of an ordered semihypergroup is introduced, and several related properties and applications are given. In particular, we discuss the relationship between the weak hyperfilters and the prime hyperideals in ordered semihypergroups. Furthermore, we define and investigate the equivalence relation $ {\mathcal W} $ on an ordered semihypergroup by weak hyperfilters. We establish the relation of the equivalence relation $ {\mathcal W} $ and Green's relations of an ordered semihypergroup. Finally, characterizations of intra-regular (duo) ordered semihypergroups are given by the properties of weak hyperfilters.
Citation: Jian Tang, Xiang-Yun Xie, Ze Gu. A study on weak hyperfilters of ordered semihypergroups[J]. AIMS Mathematics, 2021, 6(5): 4319-4330. doi: 10.3934/math.2021256
In this paper, the notion of weak hyperfilters of an ordered semihypergroup is introduced, and several related properties and applications are given. In particular, we discuss the relationship between the weak hyperfilters and the prime hyperideals in ordered semihypergroups. Furthermore, we define and investigate the equivalence relation $ {\mathcal W} $ on an ordered semihypergroup by weak hyperfilters. We establish the relation of the equivalence relation $ {\mathcal W} $ and Green's relations of an ordered semihypergroup. Finally, characterizations of intra-regular (duo) ordered semihypergroups are given by the properties of weak hyperfilters.
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Jian Tang, Xiang-Yun Xie, Ze Gu. A study on weak hyperfilters of ordered semihypergroups[J]. AIMS Mathematics, 2021, 6(5): 4319-4330. doi: 10.3934/math.2021256
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