On Quasi-semiprime and Semiprime Γ -Ideals in Ordered Γ-AG-Groupoids


  • Pairote Yiarayong
  • Phakakorn Panpho


Γ -AG-Groupoid, Ordered Γ-AG-Groupoid, Γ-ideal, semiprime Γ-ideal, quasi-semiprime Γ-ideal.


The aim of this short note is to introduce the concepts of quasi-semiprimeand semiprime Γ-ideals in ordered Γ-AG-groupoids with left identity. These concepts are related to the concepts of quasi-semiprime and semiprime Γ-ideals, play an important role in studying the structure of ordered Γ-AG-groupoids, so it seems to be interesting to study them.


Faisal N., Yaqoob A., Borumand Saeid, “Some results in bipolar-valued fuzzy ordered AG-groupoidsâ€, Discussiones Mathematicae General Algebra and Applications, vol. 32, pp. 55-57, 2012.

Faisal N., Yaqoob K., Hila, “On fuzzy (2; 2)-regular ordered $Gamma$-AG**-groupoidsâ€, U.P.B. Sci. Bull. Series A, vol. 74. no.2, pp. 87-104, 2012.

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

Khan M., Anis S., Shum K.P., “Characterizations of regular ordered Abel-Grassmann groupoidsâ€, International Journal of Algebra, vol. 5., no. 11, pp. 499-521, 2011.

Khan M., Faisal, “On fuzzy ordered Abel-Grassmann's groupoidsâ€, J. Math. Res. (3: 27 - 40, doi: 10.5539/jmr.v3n2p27), 2011.

Khan A., Faisal, Khan W., Yaqoob N., “Ordered LA-semigroups in terms of interval valued fuzzy idealsâ€, Journal of Advanced Research in Pure Mathematics, vol. 5, pp. 100-117, 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.

Khan M., Amjid V., Faisal, “Characterizations of intra-regular $Gamma$-AG**-groupoids by the properties of their $Gamma$- idealsâ€, http://arxiv.org/abs/1011.2845 (accessed: 4 September 2013).

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

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

Shah T., Inayatur-Rehman, Razzaque A., “Soft ordered Abel-Grassman's groupoid (AG-groupoid)â€, International Journal of the Physical Sciences, vol. 6., no. 25, pp. 6118-6126, 2011.

Shah T., Rehman I., “On $m$-systems in $Gamma$-AG-groupoidsâ€, Proc. Pakistan Acad.Sci., vol. 47., no. 1, pp. 33-39, 2011.

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, 2011.

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




How to Cite

Yiarayong, P., & Panpho, P. (2014). On Quasi-semiprime and Semiprime Γ -Ideals in Ordered Γ-AG-Groupoids. Asian Journal of Applied Sciences, 2(6). Retrieved from https://www.ajouronline.com/index.php/AJAS/article/view/1831

Most read articles by the same author(s)

1 2 > >>