Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings

Authors

  • Amira A. Abduljaleel Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq
  • Abdulrahman H. Majeed Department of Mathematics, College of Science, Baghdad University, Baghdad, Iraq

Keywords:

Semiprime Ring, Right (Left) Centralizer, Strong Commutativity Preserving

Abstract

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) ( ) ( ) ( ), (viii) ( ) ( ) for all .

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Published

2022-04-28

Issue

Section

Mathematics

How to Cite

Generalized Strong Commutativity Preserving Centralizers of Semiprime Rings. (2022). Iraqi Journal of Science, 57(3B), 2079-2088. https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/6941

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