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M. Daif (1998)
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Abstract In (Acta Math. Hungar. 66 (1995), 337–343), Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d ( x y ) = d ( y x ) ${d(xy)=d(yx)}$ for all x , y ∈ R ${x,y\in R}$ , then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d ( x x * ) = d ( x * x ) ${d(xx^*)=d(x^*x)}$ for all x ∈ R and S ( R ) ∩ Z ( R ) ≠ ( 0 ) ${S(R)\cap Z(R)\ne (0)}$ , then R is commutative. Moreover, some related results have also been discussed.
Georgian Mathematical Journal – de Gruyter
Published: Mar 1, 2016
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