On derivations and Lie structure of semirings

Abstract

In [8], Herstein introduced the notion of the Lie structure of associative rings and established the Lie type theory for rings. This paper extends these ring theoretical results and also extends some well known results of [3, 6, 7] in the framework of semirings, which are very important to investigate the Lie type theory of semirings and their higher commutators. Moreover, we characterize the Lie structure of semirings and thereby explore the action of derivations on Lie ideals of semirings.