Bi-$\Gamma$-hyperideals and Green's relations in ordered $\gamma$-semihypergroups
Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 63-73.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we proceed with the study of the basic properties of bi-$\Gamma$-hyperideals of ordered $\Gamma$-semihypergroups. The purpose of the present paper is to study the Green's relations on ordered $\Gamma$-semihypergroups.
@article{EMJ_2017_8_4_a7,
     author = {S. Omidi and B. Davvaz},
     title = {Bi-$\Gamma$-hyperideals and {Green's} relations in ordered $\gamma$-semihypergroups},
     journal = {Eurasian mathematical journal},
     pages = {63--73},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a7/}
}
TY  - JOUR
AU  - S. Omidi
AU  - B. Davvaz
TI  - Bi-$\Gamma$-hyperideals and Green's relations in ordered $\gamma$-semihypergroups
JO  - Eurasian mathematical journal
PY  - 2017
SP  - 63
EP  - 73
VL  - 8
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a7/
LA  - en
ID  - EMJ_2017_8_4_a7
ER  - 
%0 Journal Article
%A S. Omidi
%A B. Davvaz
%T Bi-$\Gamma$-hyperideals and Green's relations in ordered $\gamma$-semihypergroups
%J Eurasian mathematical journal
%D 2017
%P 63-73
%V 8
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a7/
%G en
%F EMJ_2017_8_4_a7
S. Omidi; B. Davvaz. Bi-$\Gamma$-hyperideals and Green's relations in ordered $\gamma$-semihypergroups. Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 63-73. http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a7/

[1] S.M. Anvariyeh, S. Mirvakili, B. Davvaz, “On $\Gamma$-hyperideals in $\Gamma$-semihypergroups”, Carpathian J. Math., 26:1 (2010), 11–23 | MR

[2] S.M. Anvariyeh, S. Mirvakili, B. Davvaz, “Pawlak's approximations in $\Gamma$-semihypergroups”, Comput. Math. Appl., 60 (2010), 45–53 | DOI | MR

[3] T. Changphas, B. Davvaz, “Bi-hyperideals and quasi-hyperideals in ordered semihypergroups”, Ital. J. Pure Appl. Math., 35 (2015), 493–508 | MR

[4] T. Changphas, B. Davvaz, “Properties of hyperideals in ordered semihypergroups”, Ital. J. Pure Appl. Math., 33 (2014), 425–432 | MR

[5] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani Editore, Italy, 1993 | MR

[6] P. Corsini, V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics, Kluwer Academic Publishers, Dordrecht, 2003 | MR

[7] B. Davvaz, V. Leoreanu-Fotea, Hyperring theory and applications, International Academic Press, USA, 2007

[8] B. Davvaz, S. Omidi, “Basic notions and properties of ordered semihyperrings”, Categ. General Alg. Structures Appl., 4 (2016), 43–62 | MR

[9] B. Davvaz, P. Corsini, T. Changphas, “Relationship between ordered semihypergroups and ordered semigroups by using pseudoorder”, European J. Combinatorics, 44 (2015), 208–217 | DOI | MR

[10] T.K. Dutta, N.C. Adhikari, “On partially ordered $\Gamma$-semigroup”, Southeast Asian Bull. Math., 28:6 (2004), 1021–1028 | MR

[11] Z. Gu, X. Tang, “Ordered regular equivalence relations on ordered semihypergroups”, J. Algebra, 450 (2016), 384–397 | DOI | MR

[12] D. Heidari, B. Davvaz, “On ordered hyperstructures”, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 73 (2011), 85–96 | MR

[13] D. Heidari, S.O. Dehkordi, B. Davvaz, “$\Gamma$-semihypergroups and their properties”, U.P.B. Sci. Bull. Series A, 72 (2010), 197–210 | MR

[14] K. Hila, “On quasi-prime, weakly quasi-prime left ideals in ordered $\Gamma$-semigroups”, Math. Slovaca, 60 (2010), 195–212 | DOI | MR

[15] A. Iampan, “Characterizing ordered bi-ideals in ordered $\Gamma$-semigroups”, Iranian Journal of Mathematical Sciences and Informatics, 4 (2009), 17–25 | MR

[16] K. Iseki, “A characterization of regular semigroups”, Proc. Japan Acad., 32 (1956), 676–677 | DOI | MR

[17] N. Kehayopulu, “On regular duo po-$\Gamma$-semigroups”, Math. Slovaca, 61 (2011), 871–884 | DOI | MR

[18] N. Kehayopulu, “On prime, weakly prime ideals in po-$\Gamma$-semigroups”, Lobachevskii J. Math., 30 (2009), 257–262 | DOI | MR

[19] N. Kehayopulu, “Green's relations and the relation $\mathcal{N}$ in $\Gamma$-semigroups”, Quasigroups Relat. Syst., 22 (2014), 89–96 | MR

[20] N. Kehayopulu, “Ordered semigroups whose elements are separated by prime ideals”, Math. Slovaca, 62 (2012), 417–424 | DOI | MR

[21] N. Kehayopulu, “On ordered $\Gamma$-semigroups”, Sci. Math. Japonica, 71 (2010), 179–185 | MR

[22] N. Kehayopulu, “On regular ordered semigroups”, Math. Japonica, 45 (1997), 549–553 | MR

[23] N. Kehayopulu, “On intra-regular ordered semigroups”, Semigroup Forum, 46 (1993), 271–278 | DOI | MR

[24] N. Kehayopulu, “Note on Green's relations in ordered semigroups”, Math. Japonica, 36 (1991), 211–214 | MR

[25] N. Kehayopulu, M. Tsingelis, “On weakly prime ideals of ordered semigroups”, Math. Japonica, 35 (1990), 1051–1056 | MR

[26] M. Kondo, N. Lekkoksung, “On intra-regular ordered $\Gamma$-semihypergroups”, Int. Journal of Math. Analysis, 7:28 (2013), 1379–1386 | DOI | MR

[27] Y.I. Kwon, “The filters of the ordered $\Gamma$-semigroups”, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math., 4 (1997), 131–135 | MR

[28] Y.I. Kwon, S. K. Lee, “On weakly prime ideals of ordered $\Gamma$-semigroups”, Comm. Korean Math. Soc., 13 (1998), 251–256 | MR

[29] F. Marty, “Sur une generalization de la notion de groupe”, 8$^{\mathrm{th}}$ Congress Math. Scandinaves (Stockholm, Sweden, 1934), 45–49

[30] B. Pibaljommee, B. Davvaz, “Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups”, J. Intell. Fuzzy Systems, 28 (2015), 2141–2148 | DOI

[31] M.K. Sen, N.K. Saha, “On $\Gamma$-semigroup I”, Bull. Calcutta Math. Soc., 78 (1986), 180–186 | MR

[32] M.K. Sen, A. Seth, “On po-$\Gamma$-semigroups”, Bull. Calcutta Math. Soc., 85 (1993), 445–450 | MR

[33] T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, Palm Harbor, Florida, 1994 | MR