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Year 2019, Volume: 7 Issue: 1, 107 - 111, 15.04.2019

Abstract

References

  • [1] Abul Basar and M. Y. Abbasi, Some Properties of Q-Fuzzy Ideals in po-G-Semigroups, Palestine Journal of Mathematics, 7(2)(2018), 505–511.
  • [2] Abul Basar, A note on intra-regular ordered G-semigroups with invo-lution, Eurasian Bulletin of Mathematics, 1(2) (2018), 78-84.
  • [3] Abul Basar and M. Y. Abbasi, On covered G-ideals in G-semigroups, Global Journal of Pure and Applied Mathematics, 13(5)(2017), 1465–1472.
  • [4] Abul Basar and M. Y. Abbasi, On generalized bi-G-ideals in G-semigroups, Quasigroups And Related Systems, 23(2015), 181–186.
  • [5] F. Yousafzai, A. Khan and B. Davvaz, On fully regular AG-groupoids, Afrika Mathematica, 25(2014), 449-459.
  • [6] F. Yousafzai, A. Khan, and A. Iampan, On (m;n)-ideals of an ordered Abel-Grassmann Groupoid, Korean J. Math., 3(23)(2015), 357-370.
  • [7] M. Akram, N. Yaqoob and M. Khan, On (m;n)-ideals in LA-semigroups, Applied mathematical Sciences, 7(2013), 2187 - 2191.
  • [8] M. A. Kazim and M. Naseeruddin, On almost semigroups, The Alig. Bull. Math., 2 (1972), 1-7.
  • [9] M. Y. Abbasi and Abul Basar, A note on ordered bi-G-ideals in intra-regular ordered G-semigroups, Afrika Mathematica, (27)(7-8) (2016), 1403–1407.
  • [10] M. Y. Abbasi and Abul Basar, On Generalizations of ideals in LA-G-semihypergroups, Southeast Asian Bulletin of Mathematics, (39) (2015), 1-12.
  • [11] M. Y. Abbasi and A. Basar, Some properties of ordered 0-minimal (0, 2)-bi-G-ideals in po-G-semigroups, Hacettepe Journal of Mathematics and Statistics, 2(44)(2015), 247–254.
  • [12] M. Y. Abbasi and Abul Basar, Weakly prime ideals in involution po-G-semigroups, Kyungpook Mathematical Journal, 54(2014), 629-638.
  • [13] N. Yaqoob and M. Aslam, Prime (m,n)bi-G-hyperideals in G-semihypergroups, Applied Mathematics and Information Sciences, 8(5) (2014), 2243-2249.
  • [14] N. Yaqoob, M. Aslam, B. Davvaz and A. B. Saeid, On rough (m,n)bi-G-hyperideals in G-semigroups, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 1 (75) (2013), 119-128.
  • [15] N. Yaqoob and R. Chinram, On prime (m,n)bi-ideals and rough prime (m,n)bi-ideals in semigroups, Far East Journal of Mathematical Sciences, 62(2) (2012), 145-159.
  • [16] Q. Mushtaq and S. M. Yusuf, On locally associative LA-semigroups,J. Nat. Sci. Math.,(19)(1979), 57-62.
  • [17] Satyanarayana Bhavanari, M. Y. Abbasi, Abul Basar and Syam Prasad Kuncham, Some Results on Abstract Affine Gamma-Near-Rings, International Journal of Pure and Applied Mathematical Sciences, 7(1) (2014), 43–49.
  • [18] T. Shah and I. Rehman, On G-ideals and bi-G-ideals in G-AG-groupoid, International Journal of Algebra, 6(4)(2010), 267-276.
  • [19] V. Amjad, K. Hila and F. Yousafzai, Generalized hyperideals in locally associative left almost semihypergroups, New York Journal of Mathematics, (20)(2014), 1063-1076.
  • [20] W. Khan, F. Yousafzai and M. Khan, On (m,n)-ideals of left almost semigroups, European Journal of Pure and Applied Mathematics, 9(3)(2016), 277-291.

A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups

Year 2019, Volume: 7 Issue: 1, 107 - 111, 15.04.2019

Abstract

In this paper, we investigate the notion of $(m, n)$-ideals in a non-associative algebraic structure, which we call an ordered $LA$-$\Gamma$-semigroup. We prove that if $(S, \Gamma, \cdot, \leq)$ is a unitary ordered $LA$-$\Gamma$-semigroup with zero and $S$ has the condition that it contains no non-zero nilpotent $(m, n)$-ideals and if $R(L)$ is a 0-minimal right (left) ideal of $S$, then either $(R\Gamma L]=\{0\}$ or $(R\Gamma L]$ is a 0-minimal $(m, n)$-ideal of $S$. Also, we prove that if $(S, \Gamma, \cdot, \leq)$ is a unitary ordered $LA$-$\Gamma$-semigroup; $A$ is an $(m, n)$-ideal of $S$ and $B$ is an $(m, n)$-ideal of $A$ such that $B$ is idempotent, then $B$ is an $(m, n)$-ideal of $S$.



References

  • [1] Abul Basar and M. Y. Abbasi, Some Properties of Q-Fuzzy Ideals in po-G-Semigroups, Palestine Journal of Mathematics, 7(2)(2018), 505–511.
  • [2] Abul Basar, A note on intra-regular ordered G-semigroups with invo-lution, Eurasian Bulletin of Mathematics, 1(2) (2018), 78-84.
  • [3] Abul Basar and M. Y. Abbasi, On covered G-ideals in G-semigroups, Global Journal of Pure and Applied Mathematics, 13(5)(2017), 1465–1472.
  • [4] Abul Basar and M. Y. Abbasi, On generalized bi-G-ideals in G-semigroups, Quasigroups And Related Systems, 23(2015), 181–186.
  • [5] F. Yousafzai, A. Khan and B. Davvaz, On fully regular AG-groupoids, Afrika Mathematica, 25(2014), 449-459.
  • [6] F. Yousafzai, A. Khan, and A. Iampan, On (m;n)-ideals of an ordered Abel-Grassmann Groupoid, Korean J. Math., 3(23)(2015), 357-370.
  • [7] M. Akram, N. Yaqoob and M. Khan, On (m;n)-ideals in LA-semigroups, Applied mathematical Sciences, 7(2013), 2187 - 2191.
  • [8] M. A. Kazim and M. Naseeruddin, On almost semigroups, The Alig. Bull. Math., 2 (1972), 1-7.
  • [9] M. Y. Abbasi and Abul Basar, A note on ordered bi-G-ideals in intra-regular ordered G-semigroups, Afrika Mathematica, (27)(7-8) (2016), 1403–1407.
  • [10] M. Y. Abbasi and Abul Basar, On Generalizations of ideals in LA-G-semihypergroups, Southeast Asian Bulletin of Mathematics, (39) (2015), 1-12.
  • [11] M. Y. Abbasi and A. Basar, Some properties of ordered 0-minimal (0, 2)-bi-G-ideals in po-G-semigroups, Hacettepe Journal of Mathematics and Statistics, 2(44)(2015), 247–254.
  • [12] M. Y. Abbasi and Abul Basar, Weakly prime ideals in involution po-G-semigroups, Kyungpook Mathematical Journal, 54(2014), 629-638.
  • [13] N. Yaqoob and M. Aslam, Prime (m,n)bi-G-hyperideals in G-semihypergroups, Applied Mathematics and Information Sciences, 8(5) (2014), 2243-2249.
  • [14] N. Yaqoob, M. Aslam, B. Davvaz and A. B. Saeid, On rough (m,n)bi-G-hyperideals in G-semigroups, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 1 (75) (2013), 119-128.
  • [15] N. Yaqoob and R. Chinram, On prime (m,n)bi-ideals and rough prime (m,n)bi-ideals in semigroups, Far East Journal of Mathematical Sciences, 62(2) (2012), 145-159.
  • [16] Q. Mushtaq and S. M. Yusuf, On locally associative LA-semigroups,J. Nat. Sci. Math.,(19)(1979), 57-62.
  • [17] Satyanarayana Bhavanari, M. Y. Abbasi, Abul Basar and Syam Prasad Kuncham, Some Results on Abstract Affine Gamma-Near-Rings, International Journal of Pure and Applied Mathematical Sciences, 7(1) (2014), 43–49.
  • [18] T. Shah and I. Rehman, On G-ideals and bi-G-ideals in G-AG-groupoid, International Journal of Algebra, 6(4)(2010), 267-276.
  • [19] V. Amjad, K. Hila and F. Yousafzai, Generalized hyperideals in locally associative left almost semihypergroups, New York Journal of Mathematics, (20)(2014), 1063-1076.
  • [20] W. Khan, F. Yousafzai and M. Khan, On (m,n)-ideals of left almost semigroups, European Journal of Pure and Applied Mathematics, 9(3)(2016), 277-291.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Abul Basar

Publication Date April 15, 2019
Submission Date November 15, 2018
Acceptance Date February 28, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Basar, A. (2019). A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp Journal of Mathematics, 7(1), 107-111.
AMA Basar A. A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp J. Math. April 2019;7(1):107-111.
Chicago Basar, Abul. “A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 107-11.
EndNote Basar A (April 1, 2019) A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp Journal of Mathematics 7 1 107–111.
IEEE A. Basar, “A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups”, Konuralp J. Math., vol. 7, no. 1, pp. 107–111, 2019.
ISNAD Basar, Abul. “A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups”. Konuralp Journal of Mathematics 7/1 (April 2019), 107-111.
JAMA Basar A. A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp J. Math. 2019;7:107–111.
MLA Basar, Abul. “A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 107-11.
Vancouver Basar A. A Note on $(m, n)$-$\Gamma$-Ideals of Ordered $LA$-$\Gamma$-Semigroups. Konuralp J. Math. 2019;7(1):107-11.
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