Glasnik Matematicki, Vol. 41, No.1 (2006), 51-55.

ON FUNCTIONAL EQUATIONS RELATED TO BICIRCULAR PROJECTIONS

Joso Vukman

Department of Mathematics, University of Maribor, PEF, Koroška 160, 2000 Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si

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 in 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 in 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 in R, and p* = p, q* = -q.

2000 Mathematics Subject Classification.   16E99.

Key words and phrases.   *-ring, semiprime ring, derivation, left (right) centralizer, bicircular projection.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.04

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