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On functional equations related to bicircular projectionsVukman, JosoIn this paper we prove the following result. Let ▫$R$▫ be a 2-torsion free semiprime ▫$\ast$▫-ring. Suppose that ▫$D, G : R \to R$▫ are additive mappings satisfying the relations ... ▫$D(xyx)=D(x)yx+xG(y^{\ast})^{\ast}x+xyD(x), G(xyx)= G(x)yx+xD(y^{\ast})^{ast}x+xyG(x)$▫ for all pairs ▫$x,y \in R$▫. In which 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 form symmetric Martindale ring of quotients of ▫$R$▫. Besides, ▫$d(x)=-d(x^{\ast})^{\ast}, g(x)=g(x^{\ast})^{\ast}$▫, for all ▫$x \in R$▫, and ▫$p^{\ast} = p,q^{\ast} = -q$▫.Source: Glasnik matematički. Serija 3. - ISSN 0017-095X (Vol. 41, 61, 2006, str. 51-55)Type of material - article, component part ; adult, seriousPublish date - 2006Language - englishCOBISS.SI-ID - 14618120
Author
Vukman, Joso
Topics
matematika |
algebra |
prakolobarji |
polprakolobarji |
odvajanje |
jordansko odvajanje |
levi centralizator |
desni centralizator |
jordanski levi centralizator |
jordanski desni centralizator |
bicirkularne projekcije |
mathematics |
algebra |
prime rings |
semiprime rings |
derivation |
Jordan derivation |
left centralizer |
right centralizer |
Jordan left centralizer |
Jordan right centralizer |
bicircular projections
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Vukman, Joso | 04310 |
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