Some Basic Properties of Γ-Abel-Grassmann's Groupoids

Authors

  • Pairote Yiarayong

Keywords:

Γ-AG-groupoid, Γ-AG*-groupoid, Γ-AG**-groupoid, Γ-cancellative AG*-groupoid, Γ-Bol*-AG-groupoid.

Abstract

In this article we investigate some basic properties of newly discovered classes of Γ-AG-groupoids. We consider three classes that include Γ-AG*-groupoids, -middle nuclear square AG-groupoids, Γ-right nuclear square AG-groupoids and Γ-Bol*-AG-groupoids. We start with the following theorem that gives a relation between Γ-AG*-groupoids,  Γ-middle nuclear square and Γ- nuclear square. We investigate that every Γ-cancellative AG*-groupoid is Γ-transitively commutative AG-groupoid.

References

Kazim M.A., Naseeruddin M., “On almost semigroupsâ€, The Alig. Bull. Math., vol. 2, pp. 1-7, 1972.

Khan M., Amjid V., Faisal, “ Characterizations of intra-regular -AG**-groupoids by the properties of their $Gamma$- idealsâ€, arXiv:1011.1364v1 [math.GR], 2010.

Khan M., Anis S., Faisal, “On Fuzzy $Gamma$-ideals of $Gamma$-Abel-Grassmann's Groupoidsâ€, Res. J. Appl. Sci. Eng. Technol., vol. 6, no. 8, pp. 1326-1334, 2013.

Khan M., Naveed Ahmad, “Characterizations of left almost semigroups by their idealsâ€, Journal of Advanced Research in Pure Mathematics, vol. 2, no. 3, pp. 61-73, 2010.

Mushtaq Q., Yousuf S.M., “On LA-semigroup defined by a commutative inverse semigroupâ€, Math. Bech., vol. 40, pp. 59-62, 1988.

Mushtaq Q., Yousuf S.M., “On LA-semigroupsâ€, The Alig. Bull. Math., vol. 8, pp. 65-70, 1978.

Naseeruddin M., “Some studies in almost semigroups and flocksâ€, Ph.D. thesis Aligarh Muslim University Aligarh India, 1970.

Protic P.V., Stevanovic N., “AG-test and some general properties of Abel-Grassmann's groupoidsâ€, PU. M. A., vol. 4, no. 6, pp. 371-383, 1995.

Sen M.K., “On $Gamma$-semigroupsâ€, Proceeding of International Symposium on Algebra and Its Applications Decker Publication New York, pp. 301-308, 1981.

Sen, M.K., Saha N.K., “On $Gamma$ -semigroups Iâ€, Bull. Cal. Math. Soc., vol. 78, pp. 180-186, 1986.

Shah M., Ahmad I., Ali A., “Discovery of new classes of AG-groupoidsâ€, Research Journal of Recent Sciences, vol. 1, no. 11, pp. 47-49, 2012.

Shah M., Ahmad I., Ali A., “On introduction of new Classes of AG-groupoidsâ€, Research Journal of Recent Sciences, vol.2, no. 123, pp. 64-66, 2013.

Shah M., Ahmad I., Ali A., “Some new results on and $Gamma$ -AG-groupoidsâ€, Research Journal of Recent Sciences, vol. 2, no. 1, pp. 67-70, 2013.

Shah T., Rehman I., “Decomposition of locally associative $Gamma$-AG-groupoidsâ€, Novi Sad J. Math., vol. 43, no. 1, pp. 1-8, 2013.

Shah T., Rehman I., “On $Gamma$ -ideals and $Gamma$ -bi-ideals in $Gamma$ -AG-Groupoidsâ€, International Journal of Algebra, vol. 4, no. 6, pp. 267-276, 2010.

Shah T., Rehman I., “On m-systems in $Gamma$-AG-groupoidsâ€, Proc. Pakistan Acad.Sci., vol. 47, no. 1, pp. 33-39, 2010.

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Published

2015-02-15

How to Cite

Yiarayong, P. (2015). Some Basic Properties of Γ-Abel-Grassmann’s Groupoids. Asian Journal of Applied Sciences, 3(1). Retrieved from https://ajouronline.com/index.php/AJAS/article/view/2170

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