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

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

Thiti Gaketem


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 $m, n \geq 3$.


LA-semigroup, ideal, $0$-minimal $(m, n)$-ideal , $(m, n)$-regular.

Subject classification

20M10, 20N99


School of Science, University of Phayao grant.

Full Text:



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

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)

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)

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

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)

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)

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)

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

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

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)

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

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)

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)

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)

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)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr