Derivable Maps of Prime Rings


Our active aim in this paper is to prove the following Let Ŕ be a ring having an idempotent element . Suppose that is a subring of Ŕ which satisfies: and . implies . implies and hence implies . implies .If is a derivable map of satisfying Then is additive. This extend Daif's result to the case need not contain any non-zero idempotent element.