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- W2067632740 abstract "Let S be a nonempty subset of a ring R. A map <TEX>$f:R{rightarrow}R$</TEX> is called strong commutativity preserving on S if [f(x), f(y)] = [x, y] for all <TEX>$x,y{in}S$</TEX>, where the symbol [x, y] denotes xy - yx. Bell and Daif proved that if a derivation D of a semiprime ring R is strong commutativity preserving on a nonzero right ideal <TEX>${rho}$</TEX> of R, then <TEX>${rho}{subseteq}Z$</TEX>, the center of R. Also they proved that if an endomorphism T of a semiprime ring R is strong commutativity preserving on a nonzero two-sided ideal I of R and not identity on the ideal <TEX>$I{cup}T^{-1}(I)$</TEX>, then R contains a nonzero central ideal. This short note shows that the conclusions of Bell and Daif are also true without the additivity of the derivation D and the endomorphism T." @default.
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- W2067632740 date "2014-07-31" @default.
- W2067632740 modified "2023-10-16" @default.
- W2067632740 title "NONADDITIVE STRONG COMMUTATIVITY PRESERVING DERIVATIONS AND ENDOMORPHISMS" @default.
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- W2067632740 doi "https://doi.org/10.4134/bkms.2014.51.4.1127" @default.
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