Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.

(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)

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. ^

Mathematics

Recommended Citation

Philip Samuel Blau, "Lie isomorphisms of prime rings" (January 1, 1996). Electronic Doctoral Dissertations for UMass Amherst. Paper AAI9709575.
http://scholarworks.umass.edu/dissertations/AAI9709575

﻿

COinS