5th International Young Scientist Congress (IYSC-2019).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Some New Results on T1, T2 and T4-AG-groupoids

Author Affiliations

  • 1Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, PAKISTAN
  • 2 Department of Mathematics, Government Post Graduate College, Mardan, PAKISTAN

Res. J. Recent Sci., Volume 2, Issue (3), Pages 64-66, February,2 (2013)

Abstract

In this article we investigate some basic properties of newly discovered classes of AG-groupoid. We consider three classes that include T1 , T2 and T4 -AG-groupoids. We prove that every 4-AG-groupoid is Bol*-AG-groupoid. We further investigate that T1 and T4-AG-groupoids are paramedial and hence are left nuclear square AG-groupoids. We also prove that T1 and T4 are transitively commutative AG-groupoids and T1-AG-3-band is a semigroup.

References

  1. Kazim M.A. and Naseerudin M., On almost semigroups Portugalian Mathematica, 36, 1, (1977)
  2. Holgate P., Groupoids satisfying a simple invertive law, Math. Stud., 61, 101-106 (1992)
  3. Cho J.R., Pusan, Jezek J. and Kepka T., Praha, Paramedial Groupoids, Czechoslovak Mathematical Journal, 49(124), (1996)
  4. Shah M., A theoretical and computational investigations of AG-groups, PhD thesis, Quaid-i-Azam University Islamabad, Pakistan (2012)
  5. Shah M., Ali A. and Ahmad I., On introduction of new classes of AG-groupoids, Res. j. of Recent Sci., 2(1), 67-70 (2013)
  6. Shah M., Ahmad I., A. Ali, Discovery of new classes of AG-groupoids, Res. J. Recent Sci. 1(11), 47-49 (2012)
  7. Ahmad I., Rashad M., and Shah M., Construction of some algebraic structures from each other, Int. Math. Forum, 7, 53-56, 2759-2766 (2012)
  8. Shah M., Ahmad I., A. Ali, On quasi-cancellativity of AG-groupoids, Int. J. Contemp. Math. Sciences, 7(42) 2065-2070 (2012)
  9. Naseeruddin M., Some studies on almost semigroups and flocks, Ph.D Thesis, The Aligarh Muslim University, India, (1970)
  10. Howie J.M., Fundamentals of Semigroup Theory, Clarendon Press, Oxford, (2003)
  11. 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)