Some Properties of AG*-groupoid

International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN. International E-Bulletin: Information/News regarding: Academics and Research

Some Properties of AG*-groupoid

Author Affiliations

¹Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, PAKISTAN
² Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, PAKISTAN

Res. J. Recent Sci., Volume 2, Issue (4), Pages 91-93, April,2 (2013)

Abstract

We prove some new results for AG^*-groupoid such as: (1) an AG^*-groupoid is a Bol^*-AG^*-groupoid, (2) an AG^*-groupoid is nuclear square AG^*-groupoid, (3) a cancellative AG^*-groupoid is transitively commutative AG-groupoid, (4) a T¹-AG-3-band is AG^*-groupoid, (5) an AG-groupoid with a left cancellative element is a -AG-groupoid, and (6) an AG^*-groupoid is left alternative AG-groupoid.

References

Kazim M.A. and Naseerudin M., On almost semigroup, Portugaliae Mathematica. 36(1) (1977)
Holgate P., Groupoids satisfying a simple invertive law, Math. Stud., 61, 101-106 (1992)
Cho J.R., Pusan J. Jezek and T. Kepka, Praha, Paramedial Groupoids, Czechoslovak Mathematical Journal, 49(124)(1996)
Shah M., Ahmad I., Ali A., On Introduction of New Classes of AG-groupoids, Res. J. Recent Sci.,2(1), 67-70 (2013)
Shah M., Ahmad I., Ali A., Discovery of New Classes of AG-groupoids, Res. J. Recent Sci.,1(11), 47-49 (2012)
Shah M., A theoretical and computational investigation of AG-groups, PhD Thesis, Department of Mathematics, Quaid-e-Azam University, Islamabad, (2012)
Ahmad I., Rashad M., and Shah M., Some new results on , T and T AG-groupoids, Res. J. Recent Sci.,2(3), 64-66 (2013)
Rashad M., Ahmad I., and Shah M., On relations between right alternative and nuclear square AG-groupoids, Int. Math. Forum, 8(5), 237–243 (2013)
Shah M., Shah T., Ali A., On the Cancellativity of AG-Groupoids, Int. Math. Forum, 6(44), 2187 – 2194 (2011)

[ref1] Kazim M.A. and Naseerudin M., On almost semigroup, Portugaliae Mathematica. 36(1) (1977)

[ref2] Holgate P., Groupoids satisfying a simple invertive law, Math. Stud., 61, 101-106 (1992)

[ref3] Cho J.R., Pusan J. Jezek and T. Kepka, Praha, Paramedial Groupoids, Czechoslovak Mathematical Journal, 49(124)(1996)

[ref4] Shah M., Ahmad I., Ali A., On Introduction of New Classes of AG-groupoids, Res. J. Recent Sci.,2(1), 67-70 (2013)

[ref5] Shah M., Ahmad I., Ali A., Discovery of New Classes of AG-groupoids, Res. J. Recent Sci.,1(11), 47-49 (2012)

[ref6] Shah M., A theoretical and computational investigation of AG-groups, PhD Thesis, Department of Mathematics, Quaid-e-Azam University, Islamabad, (2012)

[ref7] Ahmad I., Rashad M., and Shah M., Some new results on , T and T AG-groupoids, Res. J. Recent Sci.,2(3), 64-66 (2013)

[ref8] Rashad M., Ahmad I., and Shah M., On relations between right alternative and nuclear square AG-groupoids, Int. Math. Forum, 8(5), 237–243 (2013)

[ref9] Shah M., Shah T., Ali A., On the Cancellativity of AG-Groupoids, Int. Math. Forum, 6(44), 2187 – 2194 (2011)