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On additive maps of prime rings

Published online by Cambridge University Press:  17 April 2009

Matej Brešar  and
Bojan Hvala
Matej Brešar
Affiliation:
University of MariborPF, Koroška 160, 62000 Maribor, Slovenia
Bojan Hvala
Affiliation:
University of MariborPF, Koroška 160, 62000 Maribor, Slovenia
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Abstract

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Let R be a prime ring of characteristic not 2, C be the extended centroid of R, and f: R → R be an additive map. Suppose that [f(x), x2] = 0 for all x ∈ R. Then there exist λ ∈ C and an additive map ζ: R → C such that f(x) = λx + ζ(x) for all x ∈ R. In particular, if f(x)2 = x2 for all x ∈ R, then ζ = 0 and either λ = 1 or λ= -1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 377 - 381
Copyright
Copyright © Australian Mathematical Society 1995

References

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