Geodesic
Application of (m, n)-Г-Hyperideals in Characterization of LA-Г-Semihypergroups
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 135-147.

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In this paper, we study the concept of ordered (m, n)-Г-hyperideals in an ordered LA-Г-semihypergroup. We show that if (S, Г, ◦,⩽) is a unitary ordered LA-Г-semihypergroup with zero 0 and satisfies the hypothesis that it contains no non-zero nilpotent (m, n)-Г-hyperideals and if R(L) is a 0-minimal right (left) Г-hyperideal of S, then either (R◦ Г ◦L] = 0 or (R◦ Г ◦ L] is a 0-minimal (m, n)-Г-hyperideal of S. Also, we prove that if (S, Г, ◦,⩽) is a unitary ordered LA-Г-semihypergroup; A is an (m, n)-Г-hyperideal of S and B is an (m, n)-Г-hyperideal of A such that B is idempotent, then B is an (m, n)-Г-hyperideal of S.
Keywords: LA-semihypergroups, ordered LA-Г-semi-hypergroups, (m, n)-Г-hyperideals 
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Basar, Abul. Application of (m, n)-Г-Hyperideals in Characterization of LA-Г-Semihypergroups. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 1, pp. 135-147. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_1_a10/

[1] A. Basar and M.Y. Abbasi, Some properties of Q-fuzzy ideals in po-Г-semigroups, Palestine J. Math. 7 (2018) 505–511.

[2] A. Basar and M.Y. Abbasi, On covered Г-ideals in Г-semigroups, Global J. Pure and Appl. Math. 13 (2017) 1465–1472.

[3] A. Basar and M.Y. Abbasi, On generalized bi-Г-ideals in Г-semigroups, Quasigroups and Related Systems 23 (2015) 181–186.

[4] B. Davvaz, Some results on congruences in semihypergroups, Bull. Malyas. Math. Sci. So. 23 (2000) 53–58.

[5] B. Davvaz, Characterization of subsemihypergroups by various triangular norms, Czech. Math. J. 55 (2005) 923–932. doi:10.1007/s10587-005-0076-z

[6] D. Freni, Minimal order semihypergroups of type U on the right, II, J. Algebra 340 (2011) 77–80. doi:10.1016/j.jalgebra.2011.05.015

[7] D. Heidari and B. Davvaz, On ordered hyperstructures, U.P.B. Sci. Bull. Ser. A 73 (2011) 85–96.

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

[9] F. Marty, Sur uni generalization de la notion de groupe, 8th Congress Math. Scandinaves (Stockholm, 1934) 45–49.

[10] F. Yousafzai, A. Khan and B. Davvaz, On fully regular AG-groupoids, Afrika Math. 25 (2014) 449–459.

[11] F. Yousafzai, A. Khan and A. Iampan, On (m, n)-hyperideals of an ordered Abel-Grassmann groupoid, Korean J. Math. 3 (2015) 357–370.

[12] J. Chvalina, Commutative hypergroups in the sense of Marty and ordered sets, in: Proc. Summer School, Gen. Algebra ordered Sets (Olomouc, Czech Republic, 1994) 19–30.

[13] K. Hilla, B. Davvaz and K. Naka, On quasi-hyperideals in semihypergroups, Commun. Algebra 39 (2011) 41–83. doi:10.1080/00927872.2010.521932

[14] K. Hila and J. Dine, On hyperideals on left almost semihypergroups, ISRN Algebra, (2011) Article ID 953124, 1–8. doi:10.5402/2011/953124

[15] M.Y. Abbasi and A. Basar, A note on ordered bi-Г-ideals in intra-regular ordered Г-semigroups, Afrika Math. 27 (2016) 1403–1407. doi:10.1007/s13370-016-0419-y

[16] M.Y. Abbasi and A. Basar, On generalizations of ideals in LA-Г-semigroups, South. Asian Bull. Math. 39 (2015) 1–12.

[17] M.Y. Abbasi and A. Basar, Some properties of ordered 0-minimal (0, 2)-bi-Г-ideals in po-Г-semigroups, Hacettepe J. Math. and Stat. 2 (44) (2015) 247–254. doi:10.15672/HJMS.2015449100

[18] M.Y. Abbasi and A. Basar, Weakly prime ideals in involution po-Г-semigroups, Kyungpook Math. J. 54 (2014) 629–638. doi:10.5666/kmj.2014.54.4.629

[19] M.D. Salvo, D. Freni and G. Lo Faro, Fully simple semihypergroups, J. Algebra 399 (2014) 358–377. doi:10.1016/j.jalgebra.2013.09.046

[20] M. Bakhshi and R.A. Borzooei, Ordered polygroups, Ratio Math. 24 (2013) 31–40.

[21] M. Novak, EL-hyperstructures, Ratio Math. 23 (2012) 65–80.

[22] M. Akram, N. Yaqoob and M. Khan, On (m, n)-ideals in LA-semigroups, Appl. Math. Sci. 7 (2013) 2187–2191. doi:10.12988/ams.2013.13195

[23] M.A. Kazim and M. Naseeruddin, On almost semihypergroups, Alig. Bull. Math. 2 (1972) 1–7.

[24] M. Kondo and N. Lekkoksung, On intra-regular ordered Г-semihypergroups, Int. J. Math. Anal. 7 (28) (2013) 1379–1386.

[25] M.K. Sen, On Г-semigroups, Algebra and its applications, Int. Symp. (New Delhi, 1981), Lecture Notes in Pure and Applied Mathematics 91 (Decker, New York, 1984) 301–308.

[26] N. Yaqoob and M. Aslam, Prime (m,n)bi-Г-ideals in Г-semigroups, Appl. Math. Inform. Sci. 8 (2014) 2243–2249. doi:10.12785/amis/080519

[27] N. Yaqoob, P. Corsini and F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math., Article ID 510790 (2013) 10 pages. doi:10.1155/2013/510790

[28] N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc. 23 (2015) 231–235.

[29] P. Bonansinga and P. Corsini, On semihypergroup and hypergroup homomorphisms, Boll. Un. Mat. Ital. B. 1 (1982) 717–727.

[30] P. Conrad, Ordered semigroups, Nagoya Math. J. 16 (1960) 51–64. doi:10.1017/s0027763000007546

[31] P. Corsini, Sur les semi-hypergroupes, Atti Soc. Pelorit. Sci. Fis. Math. Nat. 26 (1980) 363–372.

[32] P. Corsini, Prolegomena of Hypergroup Theory, Second edition, Aviani editor, (1993).

[33] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Advances in Mathematics, Kluwer Academic Publishers (Dordrecht, 2003). doi:10.1007/978-1-4757-3714-1

[34] Q. Mushtaq and S.M. Yusuf, On locally associative LA-semigroups, J. Nat. Sci. Math. 19 (1979) 57–62.

[35] S. Bhavanari, M.Y. Abbasi, A. Basar and S. Prasad Kuncham, Some results on abstract affine gamma-near-rings, Int. J. Pure Appl. Math. Sci. 7 (2014) 43–49.

[36] T. Vougiouklis, Hyperstructures and their Representations, Hadronic Press Monographs in Mathematics (Palm Harbor Florida, 1994).

[37] T. Shah and I. Rehman, On Г-ideals and bi-Г-ideals in Г-AG-groupoid, Int. J. Alg. 6 (2010) 267–276.

[38] S. Hoskova, Upper order hypergroups as a reflective subcategory of subquasiorder hypergroups, Ital. J. Pure Appl. Math. 20 (2006) 215–222.

[39] V. Amjad, K. Hila and F. Yousafzai, Generalized ideals in locally associative left almost semihypergroups, New York J. Math. 20 (2014) 1063–1076.

[40] V. Leoreanu, About the simplifiable cyclic semihypergroups, Italian J. Pure Appl. Math. 7 (2000) 69–76.

[41] W. Khan, F. Yousafzai and M. Khan, On (m, n)-ideals of left almost semigroups, Eur. J. Pure Appl. Math. 9 (2016) 277–291.