On Г-n- (Anti ) Generalized Strong Commutativity Preserving Maps for  Semiprime Γ-Rings

Ahmed A. Abdulridha; Abdulrahman H. Majeed

doi:10.24996/ijs.2023.64.6.32

Authors

Ahmed A. Abdulridha Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Abdulrahman H. Majeed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.6.32

Keywords:

semiprime Γ-ring, extended centroid, Г-N-anti-generalized strong commutativity preserving maps

Abstract

In this study, we prove that let N be a fixed positive integer and R be a semiprime -ring with extended centroid . Suppose that additive maps such that is onto, satisfy one of the following conditions belong to Г-N- generalized strong commutativity preserving for short; (Γ-N-GSCP) on R belong to Г-N-anti-generalized strong commutativity preserving for short; (Γ-N-AGSCP) Then there exists an element and additive maps such that is of the form and when condition (i) is satisfied, and when condition (ii) is satisfied