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Lie isomorphisms of prime rings
Abstract
In this dissertation, we first characterize Lie isomorphisms $\alpha:R\longrightarrow R\sp\prime$ of prime rings when R satisfies the standard identity in 4 variables and the characteristic of R is not 2. Any such mapping is the sum of an injective map that is either a homomorphism or an anti-homomorphism of R into the central closure of $R\sp\prime$ plus an additive map of R into the extended centroid that vanishes on the commutator subgroup (R, R). Next, we obtain a similar characterization of Lie isomorphisms $\alpha:K\longrightarrow K\sp\prime$ of the skew elements of prime rings R and $R\sp\prime$ with involutions of the second kind when $R\sp\prime$ does not satisfy a generalized polynomial identity and the characteristic of R is neither 2 nor 3. In order to obtain this description of Lie isomorphisms of skew elements, we derive a general result on triadditive mappings with commuting trace.
Subject Area
Mathematics
Recommended Citation
Blau, Philip Samuel, "Lie isomorphisms of prime rings" (1996). Doctoral Dissertations Available from Proquest. AAI9709575.
https://scholarworks.umass.edu/dissertations/AAI9709575