Korean J. Math. Vol. 26 No. 1 (2018) pp.143-153
DOI: https://doi.org/10.11568/kjm.2018.26.1.143

On $0$-minimal $(m, n)$-ideal in an LA-semigroup

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Published: Mar 30, 2018
Keywords:
LA-semigroup, ideal, $0$-minimal $(m, n)$-ideal, $(m, n)$-regular.
Mathematics Subject Classification:
20M10, 20N99

Main Article Content

Thiti Gaketem
Department of Mathematics School of Science, University of Phayao Phayao, 56000, Thailand.

Abstract

In this paper, we define $0$-minimal $(m, n)$-ideals in an LA-semigroup $S$ and prove that if $R (L)$ is a 0-minimal right (left) ideal of $S$, then either $R^mL^n = \{0\}$ or $R^mL^n$ is a $0$-minimal $(m, n)$-ideal of $S$ for $m, n \geq 3$.



Article Details

Supporting Agencies

School of Science University of Phayao grant.

References

[1] M. Akram, N. Yaqoob and M. Khan, On (m,n)-ideals in LA-semigroups, Applied Mathematical Science 7 (2013), 2187–2191. Google Scholar

[2] V. Amjad, K. Hila and F. Yousafzai, Generalized hyperideals in locally associative left almost semihypergroups, New York Journal of Mathematics 20 (2014) 1063– 1076. Google Scholar

[3] M. Gulistan, N. Yaqoob and M. Shahzad, A note on Hv-LA-semigroups, University Politehnica of Bucharest Scientic Bulletin-Series A-Applied Mathematics and Physics 77 (3) (2015) 93–106. Google Scholar

[4] M. Khan,V. Amjid and Faisal, Ideals in intra-regular left almost semigroups arXiv:1012.5598v1 [math.GR], (2010), 1–10. Google Scholar

[5] M. Khan, Faisal and V. Amjid, On some classes of Abel-Grassmann’s groupoids, arXiv:1010.5965v2 [math.GR], 2(2010), 1–6. Google Scholar

[6] M. Khan, KP. Shum and M. Faisal Iqbal, Minimal ideal of Abel-Grassmann Groupoids, International Journal of Pure and Applied Mathematics 83(2013) 121–135. Google Scholar

[7] W. Khan, F. Yousafzai, and M. Khan, On generalized ideals of left almost semigroups, European Journal of Pure and Applied Mathematics. 9, 277–291. Google Scholar

[8] D.N. Krgovic, R, On (m,n)-regular seigroup Publication de L’institut mathe- matique 18 (32) (1975), 107–110. Google Scholar

[9] Q. Mushtaq and M.Khan, Ideals in left almost semigroup, arXiv:0904. 1635v1[math.GR] 2 (2009), 1–6. Google Scholar

[10] I. Rehman, N. Yaqoob and S. Nawaz, Hyperideals and hypersystems in LA-hyperrings, Songklanakarin Journal of Science and Technology 39 (5) (2017) 651–657. Google Scholar

[11] M. Sarwar (Kamran), Conditions for LA-semigroup to resemble associative structures, PhD thesis, Quaid-i-Azam University, 1993. Google Scholar

[12] M. Shabir and S. Naz, Pure spetrum of an AG-groupoid with left identity and zero, World Applied Sciences Journal 17 (2012),1759–1768. Google Scholar

[13] T. Shah, I. Rehman and R. Chinram, On M-system in ordered AG-groupoids, Far East Journal of Mathematical Science 47 (2010), 13–21 Google Scholar

[14] N. Yaqoob and M. Aslam, Prime (m,n) bi-hyperideals in-semihypergroups, Ap- plied Mathematics and Information Sciences 8 (5) (2014) 2243–2249. Google Scholar

[15] N. Yaqoob, M. Aslam, B. Davvaz and A.B. Saeid, On rough (m,n) bi-hyperideals in semihypergroups, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 75 (1) (2013) 119–128 Google Scholar