We investigate derivations in the semiring of skew Ore polynomials over an idempotent semiring. We show that multiplying each polynomial byxon left is a derivation and construct commutative idempotent semiring consisting of derivations of a skew polynomial semiring. We introduce generalized hereditary derivations as derivations acting only over the coefficients of the polynomial and construct anS-derivation in the classical sense of Jacobson. Finally, we give a description of the delta-derivations in a skew polynomial semiringS[x] and show that an arbitrary delta-derivation can be represented by a generalized hereditary derivation and anS-derivation.
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