A study on derivations of inverse semirings with involution

In this research article, we study the influence of derivations on semirings with involution which resembles with commutativity preserving mappings. The action of derivations on Lie ideals and some differential identities regarding Lie ideals are also investigated. It is proved that for any two derivations d1, d2 of a prime semiring S with involution ⋆ such that atleast one of d1, d2 is nonzero and char(S) 2, then the identity [d1(a), d2(a ⋆ )] + d2(a ◦ a ⋆ ) = 0, for all a ∈ L implies [L , S] = (0), where L is a Lie ideal of S.