Some Basic Properties of -Ideals in Ordered AG-Groupoids
Abstract
In this paper, we study and -ideals in ordered AG-groupoids with left identity. Those are extended from left and right ideals, respectively. Some characterizations of and -ideals in ordered AG-groupoids. The obtained results extend the results on AG-groupoids with left identity. Keywords : AG-groupoid, ordered AG-groupoid, -ideal, -ideal, -ideal, -idealReferences
Amjid, V., Yousafzai, F. and Iqbal, Q. (2017). Generalized ideals in ordered left almost semigroups, Afr. Mat., 28, 605–614
Birkhoff, G. (1967). Lattice Theory, American Mathematical Society. Colloquium Publications, Providence,U.S.A..
Faisal, Yaqoob, N. and Saeid, A.B. (2012). Some results in bipolar-valued fuzzy ordered AG-groupoids,Discussiones Mathematicae General Algebra and Applications, 32, 55-76.
Fuchs, L. (1963). Partially Ordered Algebraic Systems, Pergamon Press, U.K..
Holgate, P. (1992). Groupoids satisfying a simple invertive law, Math. Stud.,61, 101-106.
Kazim,M. K. and Naseeruddin, M. (1972). On almost semigroups,The Alig. Bull. Math, 2, 1-7.
Khan, M., Anis, S. and Shum, K.P. (2011). Characterizations of left regular ordered Abel-Grassmann Groupoids,International Journal of Algebra, 5(11), 499-521.
Khan, M. and Faisal. (2001). On fuzzy ordered Abel-Grassmann's groupoids, J. Math. Res.,3, 27-40.
Khan, A., Faisal, Khan, W. and Yaqoob, N. (2013). Ordered LA-semigroups in terms of interval valued fuzzy ideals, Journal of Advanced Research in Pure Mathematics, 5(1),100-117
Khan, M. and Ahmad, N. (2010). Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics, 2(3), 61-73.
Khan, M., Anis, S. and Shum, K.P.(2011). Charactterizations of regular ordered Abel-Grassmann groupoids,International Journal of Algebra, 5(1), 499-521.
Lajos, S. (1961). Generalize ideals in semigroups, Acta Scientiarum Mathematicarum. 22, 217-222.
Mushtaq, Q.(1983). Abelian groups defined by LA-semigroups, Studia Scient. Math. Hungar, 18, 427-428.
Birkhoff, G. (1967). Lattice Theory, American Mathematical Society. Colloquium Publications, Providence,U.S.A..
Faisal, Yaqoob, N. and Saeid, A.B. (2012). Some results in bipolar-valued fuzzy ordered AG-groupoids,Discussiones Mathematicae General Algebra and Applications, 32, 55-76.
Fuchs, L. (1963). Partially Ordered Algebraic Systems, Pergamon Press, U.K..
Holgate, P. (1992). Groupoids satisfying a simple invertive law, Math. Stud.,61, 101-106.
Kazim,M. K. and Naseeruddin, M. (1972). On almost semigroups,The Alig. Bull. Math, 2, 1-7.
Khan, M., Anis, S. and Shum, K.P. (2011). Characterizations of left regular ordered Abel-Grassmann Groupoids,International Journal of Algebra, 5(11), 499-521.
Khan, M. and Faisal. (2001). On fuzzy ordered Abel-Grassmann's groupoids, J. Math. Res.,3, 27-40.
Khan, A., Faisal, Khan, W. and Yaqoob, N. (2013). Ordered LA-semigroups in terms of interval valued fuzzy ideals, Journal of Advanced Research in Pure Mathematics, 5(1),100-117
Khan, M. and Ahmad, N. (2010). Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics, 2(3), 61-73.
Khan, M., Anis, S. and Shum, K.P.(2011). Charactterizations of regular ordered Abel-Grassmann groupoids,International Journal of Algebra, 5(1), 499-521.
Lajos, S. (1961). Generalize ideals in semigroups, Acta Scientiarum Mathematicarum. 22, 217-222.
Mushtaq, Q.(1983). Abelian groups defined by LA-semigroups, Studia Scient. Math. Hungar, 18, 427-428.
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2017-09-18
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