Maps Preserving Triple Product on Rings

Let R and R۰ be two unital rings such that R contains a non-trivial idempotent P۱. If R is a prime ring, we characterize the form of bijectivemap ' : R ! R۰ which satises '(ABP) = '(A)'(B)'(P), for every A;B ۲ Rand P ۲ fP۱; P۲g, where P۲ := I 􀀀 P۱ and I is the unit member of R. It isshown that ' is an isomorphism multiplied by a central element. Finally, wecharacterize the form of ' : R ! R which satises '(P)'(A)'(P) = PAP,for every A ۲ R and P ۲ fP۱; P۲g.

Keywords:

Preserver problem , Ring , Triple product , Non-trivial idempotent