Authors:
Madhu Dadhwal Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

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Neelam Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

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In this paper, centralizing (semi-centralizing) and commuting (semi-commuting) derivations of semirings are characterized. The action of these derivations on Lie ideals is also discussed and as a consequence, some significant results are proved. In addition, Posner’s commutativity theorem is generalized for Lie ideals of semirings and this result is also extended to the case of centralizing (semi-centralizing) derivations of prime semirings. Further, we observe that if there exists a skew-commuting (skew-centralizing) derivation D of S, then D = 0. It is also proved that for any two derivations d 1 and d 2 of a prime semiring S with char S ≠ 2 and x d 1 x d 2 = 0, for all xS implies either d 1 = 0 or d 2 = 0.

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Editor in Chief: László TÓTH (University of Pécs)

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  • † István GYŐRI (University of Pannonia, Veszprém)
  • János PINTZ (Rényi Institute of Mathematics)
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Mathematica Pannonica
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