Zero divisors free Γ−semiring


  • M. Murali Krishna Rao Department of Mathematics, GIT, GITAM University, VisakhEapatnam- 530 045, A.P., India.
  • B. Venkateswarlu Department of Mathematics, GST, GITAM University, Doddaballapura - 561 203, Bengaluru North, Karnataka, India


In this paper, we introduce the notion of zero divisors free Gama-semiring. we study the properties of zero divisors free Gama-semiring and characterize the
zero divisors free Gama-semiring.


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

[2] T. K. Dutta and S.K. Sardar. On the operator semirings of a G-semiring. Southeast Asian Bull. Math., 26(2)(2002), 203-213.

[3] T.K. Dutta and S. Kar. On regular ternary semirings. In K. P. Shum, Zhexian Wan, J. P. Zhang (Eds.). Advances in algebra: Proceedings of the ICM Satellite Conference in Algebra
and Related Topics (pp. 205-213), World Scientific Publ., 2003.

[4] D. H. Lehmer. A ternary analogue of abelian groups. Amer. J. of Math., 54(2)(1932), 329-338.

[5] W. G. Lister. Ternary rings. Trans. Amer. Math. Soc., 154(1971), 37-55.

[6] M. Murali Krishna Rao. G-semirings-I. Southeast Asian Bull. Math., 19 (1)(1995), 49-54.

[7] M. Murali Krishna Rao. G-semirings-II, Southeast Asian Bull. Math., 21(5)(1997), 281--287.

[8] M. Murali Krishna Rao. The Jacobson Radical of a G-semiring, Southeast Asian Bull. Math., 23 (1999) 127--134.

[9] M. Murali Krishna Rao and B. Venkateswarlu. Regular G-incline and field G-semiring. Novi Sad J. Math., 45(2)(2015), 155-171.

[10] N. Nobusawa. On a generalization of the ring theory. Osaka. J.Math., 1(1964), 81 - 89.

[11] M. K. Sen, On G-semigroup, Proc. of the Int. Conf. on Algebra and its Appl. (pp. 301-308), Decker Publication, New York 1981.

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