Muhammad Nadeem,





In this article, we discuss some functional identities of certain semirings which enable us to induce commutativitiy in them. This will be helpful to extend some remarkable results of ring theory in the canvas of semirings. We also study some other useful functional identities which are trivial in ordinary rings.


I. Bell H. E., DaifM. N., “On derivation and commutativity in prime rings”,ActaMathematicaHungarica, vol. 66,pp: 337-343, 1995.

II. Bistarelli S., MontanariU.and Rossi F., “Semiring-based constraint logic programming:syntax and semantics”,ACMTransactions on Programming Languages and Systems, vol. 23, pp:1-29, 2001.

III. Glazek, A., Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences,Kluwer, Dordrecht, 2000.

IV. Golan J. S., Semirings and Affine Equations over Them: Theory and Applications, Kluwer, Dordrecht, 2003.

V. HersteinI. N., “A note on derivations”,Canadian Mathematical Society,vol.21, pp:369-370, 1978.

VI. Javed M. A., AslamM., HussainM., “On condition (A2) of Bandletand Petrich for inverse semirings”,International Mathematical Forum,vol.59, pp: 2903-2914, 2012.

VII. Javed M.A., AslamM., “Some commutativity conditions in prime MA-semirings”, Ars Combinatoriavol.114,pp:373-384, 2014.

VIII. Pouly M. “Generic solution construction in valuation-based systems.Advances in Artificial Intelligence”,vol.6657, pp: 335-346, 2011.

IX. Karvellas P.H., “Inversivesemirings”, Journal of the Australian Mathematical Society, vol: 18, pp: 277-287,1974.

X. Posner E. C., “Derivations in prime rings”, Proceedings of the American Mathematical Society, vol. 8, pp:1093-1100, 1957.

XI. Vandiver H. S., “Note on a simple type of algebra in which cancellation law of addition does not hold”,Bulletin of The American Mathematical Society, vol. 40,pp: 914-920, 1934.

XII. VukmanJ., “Commutating and centralizing mappings in primerings”, Proceedings of the American Mathematical Society, vol.109,pp: 47-52, 1990.

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