Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 57, Issue 3, July 2016, Pages 2079-2088 | ||
| Authors | ||
| Amira A. Abduljaleel; Abdulrahman H. Majeed | ||
| Abstract | ||
| Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of 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. | ||
| Keywords | ||
| Semiprime Ring; right; Strong Commutativity Preserving | ||
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