Original scientific paper

On functional equations related to bicircular projections

Joso Vukman

Abstract

In this paper we prove the following result. Let R be a 2-torsion free semiprime *-ring. Suppose that D, G : R → R are additive mappings satisfying the relations

D(xyx) = D(x)yx + xG(y*)*x + xyD(x), G(xyx) = G(x)yx + xD(y*)*x + xyG(x),

for all pairs x, y ∈ R. In this case D and G are of the form
8D(x) = 2(d(x) + g(x)) + (p + q)x + x(p + q), 8G(x) = 2(d(x) - g(x)) + (q - p)x + x(q - p),

for all x ∈ R, where d, g are derivations of R and p, q are some elements from symmetric Martindale ring of quotients of R. Besides, d(x) = -d(x*)*, g(x) = g(x*)*, for all x ∈ R, and p* = p, q* = -q.

Keywords

*-ring; semiprime ring; derivation; left (right) centralizer; bicircular projection

Hrčak ID:

3297

URI

https://hrcak.srce.hr/3297

Publication date:

24.5.2006.

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