### (m, n)-Hyperfilters in Ordered Semihypergroups

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**Authors:**A. MAHBOOB AND N. M. KHAN

**DOI:**10.46793/KgJMat2202.307M

**Abstract:**

First, we generalize concepts of left hyperﬁlters, right hyperﬁlters and hyperﬁlters of an ordered semihypergroup by introducing concepts of left-m-hyperﬁlters, right-n-hyperﬁlters and (m,n)-hyperﬁlters of an ordered semihypergroup. Then, some properties of these generalized hyperﬁlters have been studied. Finally, left-m-hyperﬁlters (resp. right-n-hyperﬁlters, (m,n)-hyperﬁlters) of (m, 0)-regular (resp. (0,n)-regular, (m,n)-regular) ordered semihypergroups characterize in terms of their completely prime generalized (m, 0)-hyperideals (resp. (0,n)-hyperideals, (m,n)-hyperideals).

**Keywords:**

Ordered semihypergroups, left-m-hyperﬁlters, right-n-hyperﬁlters, (m,n)-hyperﬁlters.

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