Document Type : Original Article

Authors

• Fariba Kazemi
• Ali Taghavi

University of Mazandaran

Abstract

Let R be aunital prime ring with unit I which contains a non-trivial idempotent P_1. We will show that anyarbitrary not necessarily linearmap Φ:R→Rsatisfies the condition

Φ(ABP_i )=Φ(A)BP_i+AΦ(B) P_i+ABΦ(P_i ). i=1.2 (0.1)

for allA.B∈R, where P_2=I-P_1, is an additive derivation.



Let R be aunital prime ring with unit I which contains a non-trivial idempotent P_1. We will show that anyarbitrary not necessarily linearmap Φ:R→Rsatisfies the condition

Φ(ABP_i )=Φ(A)BP_i+AΦ(B) P_i+ABΦ(P_i ). i=1.2 (0.1)

for allA.B∈R, where P_2=I-P_1, is an additive derivation.

Keywords

• Jordan triple derivation, Prime &lowast
• -algebra, Additive map