Author/Authors :
abduljaleel, amira a. baghdad university - college of science - department of mathematics, iraq , majeed, abdulrahman h. baghdad university - college of science - department of mathematics, iraq
Abstract :
R. An additive mappings f,g:R→R are called right centralizer if f(xy)=xf(y) and g(xy)=xg(y) holds for all x,yϵR. In the present paper, we introduce the concepts of generalized strong commutativity centralizers preserving and generalized strong cocommutativity preserving centralizers and we prove that R contains a nonzero central ideal if any one of the following conditions holds: (i) f(x)x=xg(x), (ii) [f(x),g(y)]=0, (iii) [f(x),g(y)]=±[x,y], (iv) f(x)og(y)=0, (v) f(x)og(y)=±xoy, (vi) [f(x),g(y)]=±xoy, (vii) f(x)og(y)±xyϵZ(R), (viii) f(U)⊆Z(R) for all x,yϵU
