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On $(m,n)$-ideals of an ordered Abel-Grassmann groupoid

Aiyared Iampan|Faisal Yousafzai|Asad Khan
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2015.09|한국수학논문집 (Korean Journal of Mathematics)|제23권 제3호|pp. 357-370|DOI http://dx.doi.org/10.11568/kjm.2015.23.3.357

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키워드

ordered AG-groupoidleft invertive lawleft identity and (mn)-ideal.
주제분류수학

초록

In this paper, we introduce the concept of $(m,n)$-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of $(m,n)$-{ideals in an ordered semigroup [14]. We also study the} $(m,n)$-regular class of an ordered $\mathcal{AG}$-groupoid in terms of $(m,n)$-ideals.

Abstract

In this paper, we introduce the concept of $(m,n)$-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of $(m,n)$-{ideals in an ordered semigroup [14]. We also study the} $(m,n)$-regular class of an ordered $\mathcal{AG}$-groupoid in terms of $(m,n)$-ideals.

참고문헌 (19)

  1. M. Akram, "On (m; n)-ideals in LA-semigroups", Ap-plied mathematical Sciences, 7, pp.2187~2191 (2013)
  2. P. Holgate, "Groupoids satisfying a simple invertive law", The Math. Stud., 1-4(61), pp.101~106 (1992)
  3. M. A. Kazim, "On almost semigroups", The Alig. Bull. Math, 2, pp.1~7 (1972)
  4. M. Khan, "Minimal ideals of Abel Grassmann groupoids, to appear in Quasi-groups and related systems", ~
  5. S. Lajos, "Generalized ideals in semigroups", Acta Sci. Math, 22, pp.217~222 (1961)
  6. Q. Mushtaq, "On LA-semigroups", The Alig. Bull. Math, 8, pp.65~70 (1978)
  7. Q. Mushtaq, "On locally associative LA-semigroups", J. Nat. Sci. Math, 19, pp.57~62 (1979)
  8. Q. Mushtaq, "On LA-semigroup de ned by a commutative inverse semigroups", Math. Bech, 40, pp.59~62 (1988)
  9. Q. Mushtaq, "On LA-semigroups with weak associative law", Scienti c Khyber, 1, pp.69~71 (1989)
  10. Q. Mushtaq, "Ideals in left almost semigroups", Proceedings of 4th International Pure Mathematics Conference, pp.65~77 (2003)
  11. Q. Mushtaq, "M-systems in LA-semigroups", Southeast Asian Bull. Math, 33, pp.321~327 (2009)
  12. Q. Mushtaq, "Topological structure on LA-semigroups", Bull Malays Math. Sci, 36, pp.901~906 (2013)
  13. P. V. Protic, "AG-test and some general properties of Abel-Grassmann's groupoids", PU. M. A., 4(6), pp.371~383 (1995)
  14. J. Sanborisoot, "On Characterizations of (m; n)-regular or-dered semigroups", Far East J. Math. Sci, 65, pp.75~86 (2012)
  15. N. Stevanovic, "Composition of Abel-Grassmann's 3-bands", Novi Sad, J. Math., 2(34), pp.175~182 (2004)
  16. X. Y. Xie, "Fuzzy radicals and prime fuzzy ideals of ordered semi-groups", Inform. Sci, 178, pp.4357~4374 (2008)
  17. F. Yousafzai, "Left regular AG-groupoids in terms of fuzzy interior ideals", Afrika Mathematika, 24, pp.577~587 (2013)
  18. F. Yousafzai, "On fully regular AG-groupoids", Afrika Mathematika, 25, pp.449~459 (2014)
  19. F. Yousafzai, "On fuzzy fully regular ordered AG-groupoids", Journal of Intelligent & Fuzzy Systems, 26, pp.2973~2982 (2014)

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