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