B. VENKATESWARLU, M. Murali Krishna RAO, Y. Adi NARAYANA

Orthogonal Reverse Derivations on semiprime Γ-semirings

In this paper, we introduce the notion of reverse derivation and orthogonal reverse derivations on

Keywords:

Γ-semirings semi prime, derivations, orthogonal reverse derivations,

PDF

___

[1] Allen, P.J., A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21 (1969), 412-416.
[2] Bresar, M. and Vukman, J., On the left derivation and related mappings, Proc. Amer. Math. Soc., 10 (1990), 7-16.
[3] Dutta, T.K. and Kar, S., On regular ternary semirings, Advances in Algebra, Proceedings of the ICM Satellite Conference in Algebra and Related Topics,World Scientific, (2003) 343-355.
[4] Javed, M.A., Aslam, M. and Hussain, M., On derivations of prime Γ-semirings, Southeast Asian Bull. of Math., 37 (2013), 859-865.
[5] Lehmer, H., A ternary analogue of abelian groups, Amer. J. of Math., 59 (1932), 329-338.
[6] Lister, W.G., Ternary rings, Tran. of Amer. Math. Soc., 154 (1971), 37-55.
[7] Murali Krishna Rao, M., Γ-semirings-I, Southeast Asian Bull. of Math., 19(1) (1995), 49-54.
[8] Murali Krishna Rao, M., Γ-semirings-II, Southeast Asian Bull. of Math., 21 (1997), 281-287.
[9] Murali Krishna Rao, M. and Venkateswarlu, B., Regular Γ-semirings and field Γ-semirings, Novi Sad J. of Math., 45 (2) (2015), 155-171.
[10] Neumann, V., On regular rings, Proc. Nat. Acad. Sci., 22 (1936), 707-13.
[11] Nobusawa, N., On a generalization of the ring theory, Osaka. J. Math., 1 (1964), 81 - 89.
[12] Posner, E.C., Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
[13] Sen, M.K., On Γ-semigroup, Proc. of International Conference of algebra and its application, (1981), Decker Publicaiton, New York, 301-308.
[14] Suganthameena, N. and Chandramouleeswaran, M., Orthogonal derivations on semirings, Int. J. Of Cont. Math. Sci., 9 (2014), 645-651.
[15] Vandiver, H.S., Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math., 40 (1934), 914-921.