• GENERALIZED LEFT-DERIVATION ON SEMIRINGS

Abstract

A semiring is an algebric system (S, +,×) such that (S,+)  and (S, × ) are semigroups such that the two distributive laws hold. It has been formally introduced by H. S. Vandiver in 1934[6]. A natural example of a semiring is the set of natural numbers under usual addition and multiplication. The notion of derivations on rings is quite old and is useful in the study of integration of analysis, algebraic geometry and algebra. The study of derivation in rings, got interested only after Posner who established two striking results on derivation in prime rings [5]