On some additive mappings on division rings

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, India

2 Department of Mathematics Faculty of Science Cairo University Giza 12613, Egypt

Abstract

 Let D be a division ring such that char(D)≠2  and α,β:D→D be automorphisms of D. The main purpose of this paper is to characterizes additive maps                              
f and g satisfying the identity f(x)α(x−1)+β(x)g(x−1)=0 for all 0≠x∈D. As an application, we describe the structure of an additive map f satisfying the identity                            
f(x)α(y)+β(x)f(y)=l for all x,y∈D such that xy=a, where l,a∈D and a is nonzero. With this, many known results can be either generalized or deduced. In particular, we generalized the results proved in
\cite{C1} and \cite{C2}, respectively.                                                                                                                                                                                           

Keywords

Journal of Algebra and Related Topics
Volume 9, Issue 2
December 2021
Pages 101-110

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