- Volume 41 Issue 3
DOI QR Code
QUASI AND BI IDEALS IN LEFT ALMOST RINGS
- Hussain, Fawad (Department of Mathematics, Abbottabad University of Science and Technology) ;
- Khan, Walayat (Department of Mathematics, Hazara University) ;
- Khan, Muhammad Sajjad Ali (Department of Mathematics, Hazara University) ;
- Abdullah, Saleem (Department of Mathematics, Abdul Wali Khan University)
- Received : 2018.01.09
- Accepted : 2019.05.13
- Published : 2019.09.25
The aim of this paper is to extend the concept of quasi and bi-ideals from left almost semigroups to left almost rings which are the generalization of one sided ideals. Further, we discuss quasi and bi-ideals in regular left almost rings and intra regular left almost rings. We then explore many interesting and elegant properties of quasi and bi-ideals.
Quasi-deals;Bi-ideals;Regular left almost rings and Intra regular left almost rings
- I. Rehman, On Generalized Commutative Ring and Related Structures, PhD. Thesis., Quaid-i-Azam University, Islamabad, 2012.
- I. Rehman, M. Shah, T. Shah and A. Razzaque, On Existence of Nonassociative LA-Ring., An. St. Univ. Ovidius Constanta. 21(3) (2013), 223-228.
- F. Hussain and S. Firdous, Direct Product of Left Almost Rings., International Journal of Sciences: Basic and Applied Research. 5(2) (2016), 113-127.
- F. Hussain and W. Khan, Congruences on Left Almost Rings., International Journal of Algebra and Statistics. 4(1) (2015), 1-6. https://doi.org/10.20454/ijas.2015.896
- J. R. Cho, Pusan, J. Jezek, T. Kepka and Praha, Paramedial Groupoids, Czechoslovak Mathematical Journal, Praha. 49(124) (1996).
- M. A. Kazim and M. Naseeruddin, On Almost Semigroups, Alig. Bull. Math. 2 (1972), 1-7.
- M. Khan, V. Amjid and Faisal, Ideals in Intra-Regular Left Almost Semigroups, arXiv preprint arXiv. (2010), 1012-5598.
- M. S. Kamran, Conditions for LA-Semigroups to Resemble Associative Structures, PhD. Thesis., Quaid-i-Azam University, Islamabad, 1993. Available at http://eprints.hec.gov.pk/2370/1/2225.htm.
- M. Shah and T. Shah, Some Basic Properties of LA-Rings., International Mathematical Forum. 6(44) (2011), 2195-2199.
- P.V.Protic and N. Stevanovi, AG-test and Some General Properties of Abel-Grassmann's Groupoid, P.U.M.A. 6(4) (1995), 371-383.
- Q. Mushtaq and S.M. Yousaf, On LA-Semigroups , Alig-Bull Math. 8 (1978), 65-70.
- S.M.Yusuf, On Left Almost Ring, Proc. of 7th International Pure Math. Conference, 2006.
- T. Shah and I. Rehman, On LA-Rings of Finitely Non-Zero Functions, Int. J. Contemp.Math. Sciences. 5(5) (2010), 209-222.
- T. Shah and I. Rehman, On Characterization of LA-Rings Through Some Properties of Their Ideals., Southeast Asian Bulletin of Mathematics. 36 (2012), 695-705.