Abstract/Details

Lie isomorphisms of prime rings


1996 1996

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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.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; skew elements
Title
Lie isomorphisms of prime rings
Author
Blau, Philip Samuel
Number of pages
68
Publication year
1996
Degree date
1996
School code
0118
Source
DAI-B 57/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780591169652, 0591169657
Advisor
Martindale, W. S., III
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9709575
ProQuest document ID
304315413
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304315413
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