Paper Information

Title: 

AN ALTERNATIVE MATRIX PROOF FOR A THEOREM OF HERSTEIN

Type: PAPER
Author(s): ARIANNEZHAD M.*,EMAMI M.
 
 *DEPARTMENT OF MATHEMATICS, UNIVERSITY OF ZANJAN 45195-313, ZANJAN, IRAN
 
Name of Seminar: SEMINAR ON ALGEBRA (SALG20)
Type of Seminar:  CONFERENCE
Sponsor:  TARBIAT MOALLEM UNIVERSITY, FACULTY OF MATHEMATICAL SCIENCES AND COMPUTER
Date:  2009Volume 20
 
 
Abstract: 

Let R be a ring. If we replace the original associative product of R with their canonic Lie product, or [a,b]=ab−ba for every a,b in R, then R would be a Lie ring. With this new product the additive commutator subgroup of R or [R,R] is a Lie subring of R. Herstein has shown that in a simple ring R with characteristic unequal to 2, any Lie ideal of R either is contained in Z(R), the center of R, or contains [R,R]. He also showed that in this situation the Lie ring [R,R]/Z[R,R] is simple. Here we give an alternative matrix proof for these results. As we showed it seems that the characteristic condition can be put on a smaller set of simple rings.

 
Keyword(s): SIMPLE RING, DIVISION RING, LIE IDEAL
 
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