# Abstract/Details

## Lie isomorphisms of prime rings

1996 1996

### Abstract (summary)

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.