Simultaneous Embeddings of Finite Dimensional Division Algebras

Details Simultaneous Embeddings of Finite Dimensional Division Algebras Simultaneous Embeddings of Finite Dimensional Division Algebras

2010-09-07

arxiv.org/abs/1009.1226v1

Mathematics

Rings and Algebras

Scientific paper

A celebrated theorem of P.M.Cohn says that for any two division rings (not necessarily finite dimensional) over a field F, their amalgamated product over F is a domain which can be embedded in a division ring. Note that even with the two initial division rings begin finite dimensional over their centers, the resulting division ring is never finite dimensional over its center. Perhaps this led Lance Small to ask the following question. Assume $F_1$ and $F_2$ are fields with the same characteristic. Small asked whether any two division algebras $D_1/F_1$ and $D_2/F_2$ can be embedded in some third division algebra $E/F$. We start with a surprisingly straightforward counterexample, but then show that a positive solution exists for division algebras finitely generated over a common subfield which is either algebraically closed or the prime subfield.

Affiliated with

Also associated with

No associations

Rating

Simultaneous Embeddings of Finite Dimensional Division Algebras 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 Simultaneous Embeddings of Finite Dimensional Division Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Simultaneous Embeddings of Finite Dimensional Division Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-704500