Abstract
In this paper, we introduce the concepts of higher reverse left (resp.right) centralizer, Jordan higher reverse left (resp. right) centralizer, and Jordan triple higher reverse left (resp. right) centralizer of G-rings. We prove that every Jordan higher reverse left (resp. right) centralizer of a 2-torsion free prime G-ring M is a higher reverse left (resp. right) centralizer of M.
Highlights
Let M and be two additive Abelian groups
In this paper we define and study the concept of higher reverse left centralizer of prime -rings and we present some properties about higher reverse left centralizers one of these theorems is : Let t =i N be a Jordan higher reverse left centralizer of a 2-torsion free -ring M, such that x y x = x y x, for all x,y M and
Lemma ( 2.6 ) Let t = i N be a Jordan higher reverse left centralizer of a -ring M . for all x, y, z M, and n N, we have that the following equations hold : (i) Gn(x,y) = – Gn(y,x)
Summary
Let M and be two additive Abelian groups. Suppose that there is a mapping fromIraqi Journal of Science, 2020, Vol 61, No 9, pp: 2341-2349d(x y) = d(x) y + x d(y), for all x,y M and [5]. Right) centralizer of a -ring M is an additive mapping t : M M which satisfies the following equation t(x y) = t(x) y Right) Jordan centralizer of a -ring M is an additive mapping t : M M which satisfies the following equation t (x x) = t(x) x
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