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On Properties of Generalized Bi-Γ-Ideals of Γ-Semirings

Authors: Teerayut Chomchuen, Aiyared Iampan


The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.

Keywords: Γ-semiring, bi-Γ-ideal, generalized bi-Γ-ideal.

Digital Object Identifier (DOI):

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[1] R. Chinram, A note on quasi-ideals in Γ-semirings, International Mathematical Forum 26 (2008), 1253–1259.
[2] ¨O. Bektas¸, N. Bayrak, and A. Ersoy, Soft Γ-semirings, arXiv:1202.1496 (math.RA), 7 Feb 2012.
[3] T. K. Dutta and S. K. Sardar, Semiprime ideals and irreducible ideals of Γ-semirings, Novi Sad Journal of Mathematics 30 (2000), 97–108.
[4] T. K. Dutta, S. K. Sardar, and S. Goswami, Operations on fuzzy ideals of Γ-semirings, arXiv:1101.4791 (math.RA), 25 Jan 2011.
[5] J. Ghosh and T. K. Samanta, Fuzzy ideals in Γ-semiring, arXiv:1010.2469 (math.GM), 12 Oct 2010.
[6] R. D. Jagatap and Y. S. Pawar, Quasi-ideals and minimal quasi-ideals in Γ-semirings, Novi Sad Journal of Mathematics 39 (2009), 79–87.
[7] J. P. Kaushik, M. A. Ansari, and M. R. Khan, On bi-Γ-ideal in Γ-semirings, International Journal of Contemporary Mathematical Sciences 3 (2008), 1255–1260.
[8] S. Lajos, Notes on generalized bi-ideals in semigroups, Soochow Journal of Mathematics 10 (1984), 55–59.
[9] S. Pianskool, S. Sangwirotjanapat, and S. Tipyota, Valuation Γ-semirings and valuation Γ-ideals, Thai Journal of Mathematics Special Issue (Annual Meeting in Mathematics) (2008), 93–102.
[10] M. Murali Krishna Rao, Γ-semiring I, Southeast Asian Bulletin of Mathematics 19 (1995), 49–54.
[11] S. K. Sardar and U. Dasgupta, On primitive Γ-semirings, Novi Sad Journal of Mathematics 34 (2004), 1–12.
[12] F. A. Sz´asz, Generalized biideals of rings I, Mathematische Nachrichten 47 (1970), 355–360.
[13] F. A. Sz´asz, Generalized biideals of rings II, Mathematische Nachrichten 47 (1970), 361–364.