ผู้วิจัย

WICHAYAPORN JANTANAN RONNASON CHINRAM AND PATTARAWAN PETCHKAEW

บทคัดย่อ

In this paper, we introduce the concepts of m-left-Γ-ideals, n-right-Γ-ideals and (m,n)-quasi-Γ-ideals in ordered LA-Γ-semigroups and investigate about some properties of those ideals. We show that the intersection of an m-left-Γ-ideal and an n-right-Γ-ideal of an ordered LA-Γ-semigroup is an (m,n)-quasi-Γ-ideal. In addition, we introduce the notion of the (m,n) intersection property in ordered LA-Γ-semigroups and prove that every (m,n)- quasi-Γ-ideal in an ordered LA-Γ-semigroup with left identity has the (m,n) intersection property.

บรรณานุกรม

[1] C. Akin, Fuzzy LA-(m,n)-Γ-ideals in LA-Γ-semigroups. Adv. Fuzzy Sets Syst. 4(6) (2017), 211-223. [2] M.A. Ansari, Roughness applied to generalized Γ-ideals of ordered LA Γ-ideals. Commu. Math. Appl. 10(1) (2019), 71-84. [3] M.A. Ansari, M.R. Khan, J.P. Kaushik, A note on (m,n)-quasi-ideals in semigroups, Int. J. Math. Anal. 38 (2009), 1853-1858. [4] A. Basar, A note on (m,n)-Γ-ideals of ordered LA-Γ-semigroups, Konuralp J. Math. 7(1) (2019), 107-111. [5] T. Gaketem, On (m,n)-quasi-ideals in LA-semigroups, Appl. Sci. 17 (2015), 57-61. [6] M.A. Kazim, N. Naseeruddin, On almost semigroups, Alig. Bull. Math. 2(1) (1972), 1-7. [7] M. Khan, V.Amjid, G. Zaman, N. Yaqoob, Characterizations of ordered Γ-Aber-Grassmann’s Groupoids, Discuss. Math., Gen. Algebra Appl. 34(1) (2014), 55-73. [8] M. Khan, F. Smarandache, S. Anis, Theory of Abel Grassmann’s groupoids, Educational Publisher, Columbus, 2015. [9] M.K. Sen, On Γ-semigroups, In: Proceeding of International Symposium on Algebra and Its Applications. Decker Publication, New York, (1981), 301-308. [10] T. Shah, I. Rehman, On Γ-ideals and Γ-bi-ideals in Γ-AG-groupoids, Int. J. Algebra, 4(6) (2010), 267-276. [11] T. Shah, I. Rehman, R. Chinram, On M-systems in ordered AG-groupoids, Far East J. Math. Sci. 47(1) (2010), 13-21. [12] O. Steinfeld, Uber die quasiideale von halbgruppen, Publ. Math. Debrecen. 4(1) (1956), 262-275.

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