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An Introduction of Theory of Involutions in Ordered Semihypergroups and their Weakly Prime Hyperideals
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In this paper, we introduce ordered semihypergroups with involution and weakly prime semihyperideal, then we investigate some properties of prime, semiprime and weakly prime hyperideals in ordered semihypergroup with involution. Also, we study intra-regular ordered semihypergroups with involution. We prove that in ordered semihypergroup S with involution such that the involution preserves the order, a semihyperideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime hyperideals of S coincide. Finally, we show that if S is an ordered semi- hypergroup with order preserving involution, then the semihyperideals of S are prime if and only if it is intra-regular.
Keywords
Semigroup, Ordered Semihypergroup, Hyperideal, Involution, Weakly Prime Hyperideal.
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- A. Hasankhani, Ideals in a semihypergroup and Green’s relations, Ratio Math., 13(1999), 29-36.
- B. Davvaz and N. S. Poursalavati, Semihypergroups and S-hypersystems, Pure Math. Appl., 11 (2000), 43-49.
- D. Fasino and D. Freni, Existence of proper semihypergroups of type U on the right, Discrete Math., 307 (2007), 2826-2836.
- F. Marty, Sur un generalisation de la notion de groupe, Huitieme Congres des mathematiciens Scand., Stockholm (1934), 45-49.
- G. Szasz, Eine Charakteristik der Primidealhalbgruppen, Publ. Math. Debrecen, 17(1970), 209-213.
- J. Nieminen, Join space graphs, J. Geom., 33 (1988), 99-103.
- M. Petrich, Introduction to Semigroups, Merill, Columbus, (1973).
- M. Y. Abbasi and Abul Basar, Weakly prime ideals in involution po-Γ-semigroups, Kyungpook Mathematical Journal, 54(2014), 629-638.
- N. H. McCoy, Prime ideals of general rings, Amer. J. Math., 71(1949), 823-833.
- N. Kehayopulu, On weakly prime ideals of ordered semigroups, Math. Japon., 26(3)(1990), 1051-1056.
- N. Kehayopulu, On prime, weakly prime ideals in ordered semigroups, Semigroup Forum, 44 (1992), 341-346.
- N. Kehayopulu, On intra-regular ordered semigroups, Semigroup Forum, 46(1993), 271-278.
- O. Steinfeld, Remark on a paper of N. H. McCoy, Publ. Math. Debrecen, 54(3)(1953), 171-173.
- P. Bonansinga and P. Corsini, On semihypergroup and hypergroup homomorphisms, Boll. Un. Mat. Ital.,1(6) (1982), 717-727.
- S. M. Anvariyeh, S. Mirvakili and B. Davvaz, On Γ-hyperideals in Γ-semihypergroups, Carpathian J. Math., 26(1) (2010), 11 - 23.
- T. Changphas and B. Davvaz, Bi-hyperideals and quasi-hyper ideals in ordered semi-hypergroups, Italian journal of pure and applied mathematics, 35(2015), 493-508.
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