BibTex RIS Cite

ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS

Year 2016, Volume: 29 Issue: 1, 143 - 148, 21.03.2016

Abstract

In this paper, we study left ideals, left primary and weakly left primary ideals in $\Gamma$-LA-rings. Some characterizations of left primary and weakly left primary ideals are obtained. Moreover, we investigate relationships left primary and weakly left primary ideals in $\Gamma$-LA-rings. Finally, we obtain necessary and sufficient conditions of a weakly left primary ideal to be a left primary ideals in $\Gamma$-LA- rings.

References

  • M.A. Kazim and M. Naseeruddin, On almost semigroups, The Alig. Bull. Math., 2(1972), 1-7.
  • M. Khan, V. Amjid and Faisal, Characterizations of intra-regular -AG**-groupoids by the properties of their -ideals, arXiv:1011.1364v1 [math.GR], (2010).
  • M. Khan and Naveed Ahmad, Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics, 2(3)(2010), 61-73.
  • Q. Mushtaq and S.M. Yousuf, On LA-semigroups, The Alig. Bull. Math., 8(1978), 65-70.
  • Q. Mushtaq and S.M. Yousuf, On LA-semigroup defined by a commutative inverse semigroup, Math. Bech., 40(1988), 59-62. [6] M. Naseeruddin, Some semigroups and flocks, Ph.D. thesis Aligarh Muslim University Aligarh India, (1970). almost
  • P.V. Protic and N. Stevanovic, AG-test and some general properties of Abel-Grassmann's groupoids, PU. M. A., 4(6)(1995), 371-383.
  • I. Rehman, M. Shah, T. Shah and A. Razzaque, On existence of nonassociative LA-ring, Analele Stiintfice ale Universitatii Ovidius Constanta, 21(3)(2013), 223-228.
  • M.K. Sen, On -semigroups, Proceeding of International Symposium on Algebra and Its Applications Decker Publication New York, (1981), 301-308.
  • M.K. Sen and N.K. Saha, On -semigroups I, Bull. Cal. Math. Soc., 78(1986), 180-186.
  • T. Shah, G. Ali and Fazal ur Rehman, Direct sum of ideals in a generalized LA-ring, International Mathematical Forum, 6(22) (2011), 1095-1101.
  • T. Shah, Fazal ur Rehman and M. Raees, On Near Left Almost Rings, (to appear).
  • T. Shah, N. Kausar and I. Rehman, fuzzy normal subrings over a nonassociative ring, Analele Stiintfice ale Universitatii Ovidius Constanta, 20(1)(2012), 369–386.
  • T. Shah and I. Rehman, On -Ideals and -Bi- Ideals in -AG-groupoids, International Journal of Algebra, 4(6)(2010), 267-276.
  • T. Shah and I. Rehman, On LA-rings of finitely nonzero functions, Int. J. Contemp. Math. Sciences, 5(5) (2010), 209-222.
  • M. Shah and T. Shah, Some basic properties of LA- ring, 6(44)(2011), 2195-2199. Forum,

LA- Rings

Year 2016, Volume: 29 Issue: 1, 143 - 148, 21.03.2016

Abstract

References

  • M.A. Kazim and M. Naseeruddin, On almost semigroups, The Alig. Bull. Math., 2(1972), 1-7.
  • M. Khan, V. Amjid and Faisal, Characterizations of intra-regular -AG**-groupoids by the properties of their -ideals, arXiv:1011.1364v1 [math.GR], (2010).
  • M. Khan and Naveed Ahmad, Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics, 2(3)(2010), 61-73.
  • Q. Mushtaq and S.M. Yousuf, On LA-semigroups, The Alig. Bull. Math., 8(1978), 65-70.
  • Q. Mushtaq and S.M. Yousuf, On LA-semigroup defined by a commutative inverse semigroup, Math. Bech., 40(1988), 59-62. [6] M. Naseeruddin, Some semigroups and flocks, Ph.D. thesis Aligarh Muslim University Aligarh India, (1970). almost
  • P.V. Protic and N. Stevanovic, AG-test and some general properties of Abel-Grassmann's groupoids, PU. M. A., 4(6)(1995), 371-383.
  • I. Rehman, M. Shah, T. Shah and A. Razzaque, On existence of nonassociative LA-ring, Analele Stiintfice ale Universitatii Ovidius Constanta, 21(3)(2013), 223-228.
  • M.K. Sen, On -semigroups, Proceeding of International Symposium on Algebra and Its Applications Decker Publication New York, (1981), 301-308.
  • M.K. Sen and N.K. Saha, On -semigroups I, Bull. Cal. Math. Soc., 78(1986), 180-186.
  • T. Shah, G. Ali and Fazal ur Rehman, Direct sum of ideals in a generalized LA-ring, International Mathematical Forum, 6(22) (2011), 1095-1101.
  • T. Shah, Fazal ur Rehman and M. Raees, On Near Left Almost Rings, (to appear).
  • T. Shah, N. Kausar and I. Rehman, fuzzy normal subrings over a nonassociative ring, Analele Stiintfice ale Universitatii Ovidius Constanta, 20(1)(2012), 369–386.
  • T. Shah and I. Rehman, On -Ideals and -Bi- Ideals in -AG-groupoids, International Journal of Algebra, 4(6)(2010), 267-276.
  • T. Shah and I. Rehman, On LA-rings of finitely nonzero functions, Int. J. Contemp. Math. Sciences, 5(5) (2010), 209-222.
  • M. Shah and T. Shah, Some basic properties of LA- ring, 6(44)(2011), 2195-2199. Forum,
There are 15 citations in total.

Details

Journal Section Mathematics
Authors

Pairote Yiarayong

Publication Date March 21, 2016
Published in Issue Year 2016 Volume: 29 Issue: 1

Cite

APA Yiarayong, P. (2016). ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS. Gazi University Journal of Science, 29(1), 143-148.
AMA Yiarayong P. ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS. Gazi University Journal of Science. March 2016;29(1):143-148.
Chicago Yiarayong, Pairote. “ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS”. Gazi University Journal of Science 29, no. 1 (March 2016): 143-48.
EndNote Yiarayong P (March 1, 2016) ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS. Gazi University Journal of Science 29 1 143–148.
IEEE P. Yiarayong, “ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS”, Gazi University Journal of Science, vol. 29, no. 1, pp. 143–148, 2016.
ISNAD Yiarayong, Pairote. “ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS”. Gazi University Journal of Science 29/1 (March 2016), 143-148.
JAMA Yiarayong P. ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS. Gazi University Journal of Science. 2016;29:143–148.
MLA Yiarayong, Pairote. “ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS”. Gazi University Journal of Science, vol. 29, no. 1, 2016, pp. 143-8.
Vancouver Yiarayong P. ON LEFT PRIMARY AND WEAKLY LEFT PRIMARY IDEALS IN $\GAMMA$-LA- RINGS. Gazi University Journal of Science. 2016;29(1):143-8.