Geodesic
Reverse derivations and generalized reverse derivations in semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 217-232

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In this article we extend the results on reverse derivation in rings to semirings. First we dispose of reverse derivations in prime semirings analogous to Herstein's result [7]. Then, we prove that reverse derivation is just an ordinary derivation in semiprime semirings if and only if it is a central derivation. We also define generalized reverse derivations and obtain some commutativity results which extend the results in [11]. The primary technique we use in these results is the use of derivations and reverse derivations in ring of differences R^Δ corresponding to the semiring R and the fact that R is embedded in R^Δ. This fact allows us to travel back and forth between R and R^Δ and serve as a key tool in obtaining the desired results.
Keywords: Reverse derivations, derivations, semirings, l-generalized reverse derivations, r-generalized reverse derivations, generalized reverse derivations and semiprime semirings 
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Swaminathan, Ganesh; Venkatachalam, Selvan. Reverse derivations and generalized reverse derivations in semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 217-232. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a13/