- LandOfFree
- Scientists
- Mathematics
- Rings and Algebras
Details
The additive group of a Lie nilpotent associative ring
The additive group of a Lie nilpotent associative ring
2012-04-12
-
arxiv.org/abs/1204.2674v1
Mathematics
Rings and Algebras
Scientific paper
Let Z be the free unitary associative ring on the set X = {x_1,x_2,...}. Define a left-normed commutator [x_1,x_2,...,x_n] by [a,b] = ab - ba, [a,b,c] = [[a,b],c]. For n \ge 2, let T^(n) be the ideal in Z generated by all commutators [a_1,a_2,...,a_n] (a_i \in Z). It can be easily seen that the additive group of the quotient ring Z/T^(2) is a free abelian group. Recently Bhupatiraju, Etingof, Jordan, Kuszmaul and Li have proved that the additive group of Z/T^(3) is free abelian as well. In the present note we show that this is not the case for Z/T^(4). More precisely, let v = [x_1,x_2,x_3][x_4,x_5]; we prove that 3v \in T^(4) but v \notin T^(4). Thus, the additive group of the quotient ring Z/T^(4) contains elements of order 3.
Affiliated with
Also associated with
No associations
LandOfFree
Say what you really think
Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.
Rating
The additive group of a Lie nilpotent associative ring does not yet have a rating.
At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The additive group of a Lie nilpotent associative ring, we encourage you to share that experience with our LandOfFree.com community.
Your opinion is very important and The additive group of a Lie nilpotent associative ring will most certainly appreciate the feedback.
Rate now
Profile ID: LFWR-SCP-O-312237
All data on this website is collected from public sources.
Our data reflects the most accurate information available at the time of publication.