Left bi-quasi ideals of semirings


  • M. Murali Krishna Rao Department of Mathematics, GIT, GITAM University, Visakhapatnam- 530 045, A.P., India.


In this paper, we introduce the notion of left (right) bi-quasi ideal
and bi-quasi ideal of semiring which are generalizations of bi-ideal and quasi ideal of semiring. Also we study the properties of bi-quasi ideals, left bi-quasi ideals and characterize the left bi-quasi simple semring and regular semiring.


[1] P. J. Allen. A fundamental theorem of homomorphism for semirings. Proc. Amer. Math. Sco., 21(2)(1969), 412--416.

[2] S. M. Ali and A. Batod. A note on quasi ideal in semirings. Southeast Asian Bull. Math., 27(5)(2004), 923-928.

[3] R. A. Good and D. R. Hughes. Associated groups for a semigroup. In E.G.Begle (Ed.) Summer miting in East Lansing (Abstract. pp 624-625) Bull. Amer. Math. Soc., 58(1952),

[4] M. Henriksen. Ideals in semirings with commutative addition. Notices of the American Mathematical Society, 6(1958), 321

[5] K. Iseki. Quasi-ideals in semirings without zero. Proc. Japan Acad., 34(2)(1958), 79-84.

[6] K. Iseki. Ideal theory of semiring. Proc. Japan Acad., 32(8)(1956), 554-559.

[7] K. Iseki. Ideal in semirings. Proc. Japan Acad., 34(1)(1958), 29-31.

[8] R. D. Jagatap and Y.S. Pawar. Quasi-ideals and minimal quasi-ideals in G-semirings. Novi Sad J. Math., 39(2)(2009), 79-87.

[9] S. Lajos. On the bi-ideals in semigroups. Proc. Japan Acad., 45(8)(1969), 710-712.

[10] S. Lajos. Generalized ideals in semigroups. Acta Sci. Math., 22(1961), 217-222.

[11] S. Lajos and F. A. Szasz. On the bi-ideals in associative ring. Proc. Japan Acad., 46(6)(1970), 505-507.

[12] Marapureddy Murali Krishna Rao. Bi-quasi-ideals and fuzzy bi-quasi{ideals of G-semigroups. Bull. Int. Math. Virtual Inst., Vol. 7(2)(2017), 231-242.

[13] O. Steinfeld. Uher die quasi ideals, Von halbgruppend. Publ. Math., Debrecen, 4(1956), 262- 275.

[14] O. Steinfeld. On ideal quotients and prime ideals. Acta Math. Hungar., 4(3-4)(1953), 288-298.

[15] H. S. Vandiver. Note on a simple type of algebra in which cancellation law of addition does not hold. Bull. Amer. Math. Soc., 40(12)(1934), 914-920.