Abstract
Let be an ordered semihypergroup and . We denote by the hyperfilter of generated by . Define an equivalence relation on . In this note, we show that is the intersection of the relations or , where runs over the completely prime hyperideals of . Moreover, we give some results on ordered semihypergroups.
Keywords
Ordered semihypergroup completely prime hyperideal hyperfilter semilattice equivalence relation ≔ {( ) ∈ × | ∈ or ∉ } where runs over the completely prime
References
- T. Changphas and B. Davvaz, Bi-hyperideals and quasi-hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 35 (2015), 493-508.
- T. Changphas and B. Davvaz, Properties of hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 33 (2014), 425-432.
- P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani Editore, Italy, 1993.
- B. Davvaz, Some results on congruences in semihypergroups, Bull. Malays. Math. Sci. So. (2), 23 (2000), 53-58.
- B. Davvaz and S. Omidi, Basic notions and properties of ordered semihyperrings, Categ. General Alg. Structures Appl. 4(1) (2016), 43-62.
- B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseudoorder, European J. Combinatorics, 44 (2015), 208-217.
- Z. Gu and X. Tang, Ordered regular equivalence relations on ordered semihypergroups, J. Algebra, 450 (2016), 384-397.
- D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A. 73(2) (2011), 85-96.
- N. Kehayopulu, Green’s relations and the relation in Γ-semigroups, Quasigroups Relat. Syst. 22 (2014), 89-96.
- F. Marty, Sur une generalization de la notion de groupe, Stockholm, 1934, 45-49. Math. Scandinaves,
- M. Siripitukdet and A. Iampan, On the least (ordered) semilattice congruence in ordered Γ-semigroups, Thai J. Math. 4 (2006), 403-415.
- J. Tang, B. Davvaz and Y. F. Luo, Hyperfilters and fuzzy hyperfilters of ordered semihypergroups, J. Intell. Fuzzy Systems, 29(1) (2015), 75-84.
Abstract
References
- T. Changphas and B. Davvaz, Bi-hyperideals and quasi-hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 35 (2015), 493-508.
- T. Changphas and B. Davvaz, Properties of hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 33 (2014), 425-432.
- P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani Editore, Italy, 1993.
- B. Davvaz, Some results on congruences in semihypergroups, Bull. Malays. Math. Sci. So. (2), 23 (2000), 53-58.
- B. Davvaz and S. Omidi, Basic notions and properties of ordered semihyperrings, Categ. General Alg. Structures Appl. 4(1) (2016), 43-62.
- B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseudoorder, European J. Combinatorics, 44 (2015), 208-217.
- Z. Gu and X. Tang, Ordered regular equivalence relations on ordered semihypergroups, J. Algebra, 450 (2016), 384-397.
- D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Series A. 73(2) (2011), 85-96.
- N. Kehayopulu, Green’s relations and the relation in Γ-semigroups, Quasigroups Relat. Syst. 22 (2014), 89-96.
- F. Marty, Sur une generalization de la notion de groupe, Stockholm, 1934, 45-49. Math. Scandinaves,
- M. Siripitukdet and A. Iampan, On the least (ordered) semilattice congruence in ordered Γ-semigroups, Thai J. Math. 4 (2006), 403-415.
- J. Tang, B. Davvaz and Y. F. Luo, Hyperfilters and fuzzy hyperfilters of ordered semihypergroups, J. Intell. Fuzzy Systems, 29(1) (2015), 75-84.
Details
| Journal Section | Mathematics |
|---|---|
| Authors | |
| Publication Date | September 30, 2016 |
| Published in Issue | Year 2016 Volume: 29 Issue: 3 |