Generalized strong commutativity preserving centralizers of semiprime rings

الملخص EN

Let R be a semiprime ring with center Z(R) and U be a nonzero ideal of R.

An additive mappings are called right centralizer if ( ) ( ) and ( ) ( ) holds for all .

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) ( ) ( ), (ii) [ ( ) ( )] , (iii) [ ( ) ( )] [ ], (iv) ( ) ( ) , (v) ( ) ( ) , (vi) [ ( ) ( )] , (vii) ( ) ( ) ( ),