(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.
References:
[1] T. Changphas and B. Davvaz, Bi-hyperdeals and quasi-hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 35 (2015), 493–508.
[2] T. Changphas and B. Davvaz, Properties of hyperideals in ordered semihypergroups, Italian Journal of Pure and Applied Mathematics 33 (2014), 425–443.
[3] B. Davvaz, W. A. Dudek and T. Vougiouklis, A Generalization of n-ary algebraic systems, Comm. Algebra 37 (2009), 1248–1263.
[4] Z. Gu and X. Tang, Ordered regular equivalence relations on ordered semihypergroups, J. Algebra 450 (2016), 384–397.
[5] K. Hila, B. Davvaz and K. Naka, On quasi-hyperideals in semihypergroups, Comm. Algebra 39 (2011), 4183–4194.
[6] D. Heidari and B. Davvaz, On ordered hyperstructures, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 73(2) (2011), 85–96.
[7] N. Kehayopulu, On weakly commutative poe-semigroups, Semigroup Forum 34 (1987), 367–370.
[8] N. Kehayopulu, Remark on ordered semigroups, Math. Japon. 35 (1990), 1061–1063.
[9] A. Mahboob, N. M. Khan and B. Davvaz, (m,n)-hyperideals in ordered semihypergroups, Categ. Gen. Algebr. Struct. Appl. (to appear).
[10] S. Lajos, Generalized ideals in semigroups, Acta Sci. Math. 22 (1961), 217–222.
[11] S. K. Lee and S. S. Lee, Left (right)-filters on po-semigroups, Kangweon Kyungki Mathematical Journal 8(1) (2000), 43–45.
[12] F. Marty, Sur une generalization de la notion de group, 8th Congres Math. Scandinaves, Stockholm, 1934, 45–49.
[13] S. Omidi and B. Davvaz, A short note on the relation ???? in ordered semihypergroups, Gazi University Journal of Science 29(3) (2016), 659–662.
[14] J. Tang, B. Davvaz and Y. Luo, Hyperfilters and fuzzy hyperfilters of ordered semihypergroups, Journal of Intelligent and Fuzzy Systems 29(1) (2015), 75–84.
[15] J. Tang, B. Davvaz and X. Y. Xie, An investigation on hyper S-posets over ordered semihypergroups, Open Math. 15 (2017), 37–56.
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