The Bi-Ideals in left almost Rings

Authors

  • Pairote Yiarayong
  • Supapon Webchasad
  • Wanchaloem Dorchana

Keywords:

left almost semiring, bi-ideal, quasi-ideal, left ideal, ideal

Abstract

In this study we promoted some notion of a left almost semiring defined in (Mrudula Devi and Sobha Latha, 2015) and further established the substructures, operations on substructures of left almost semirings. We also indicated the non similarity of a left almost semiring to the usual notion of a semiring.

 

References

D.M. Devi and G.S. Latha, LA-semirings satisfying the identity ab=a+b+1, IJISET-International Journal of Innovative Science, Engineering & Technology, 2(2015), pp. 378 - 389.

P. Holgate, Groupoids satisfying a simple invertive law, Mathematical Studies, 61(1992), pp. 101 - 106.

M.K. Kazim and M. Naseeruddin, On almost semigroups, The Aligarh Bulletin of Mathematics, 2(1972), pp. 1 - 7.

R. Kellil, On inverses of left almost semirings and strong left almost semirings, Journal of Mathematical Sciences Advances and Applications, 26(2014), pp. 29 - 39

M. Khan, and N. Ahmad, Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics, 2(3) (2010), pp. 61 - 733.

Q. Mushtaq, Abelian groups defined by LA-semigroups, Studia Scientiarum Mathematicarum Hungarica, 18(1983), pp. 427 - 428.

Q. Mushtaq and Q. Iqbal, Decomposition of a locally associative LA-semigroup, Semigroup Forum, 41(1990), pp. 154 - 164.

Q. Mushtaq and M. Iqbal, On representation theorem for inverse LA-semigroups, Proceedings of the Pakistan Academy of Sciences, 30(1993), pp. 247 - 253.

Q. Mushtaq and M. Khan, Ideals in left almost semigroup, arXiv:0904.1635v1 [math.GR], (2009).

T. Shah, T. Rehman and A. Razzaque, Soft ordered Abel-Grassman's groupoid (AG-groupoid), International Journal of the Physical Sciences, 6(25)(2011), pp. 6118 - 6126.

T. Shah and I. Rehman, On LA-rings of finitely nonzero functions, Journal of Contemporary Mathematical Sciences, 5(5) (2010), pp. 209 - 222.

M. Shah and T. Shah, Some basic properties of LA-ring, International Mathematical Forum, 6(44)(2011), pp. 2195 - 2199.

S.M. Yusuf, On left almost ring, Proc. of 7th International Pure Mathematics Conference, (2006).

Downloads

Published

2016-11-08

How to Cite

Yiarayong, P., Webchasad, S., & Dorchana, W. (2016). The Bi-Ideals in left almost Rings. Asian Journal of Applied Sciences, 4(5). Retrieved from https://ajouronline.com/index.php/AJAS/article/view/4238