Embedding domains in division rings
Università degli Studi dell'Insubria,
Universitat Autònoma de Barcelona
Suppose we have a domain embedded in a division ring . We
, and for
the smallest division ring that contains inside .
, the inversion height of inside as if there is
such that is a division ring.
Let be a commutative field. Suppose
is a ring
homomorphism which is not onto. Let
Consider the skew polynomial ring It was proved by Jategaonkar that the -algebra
generated by and is a free -algebra
We call these embeddings
- Jategaonkar embeddings have at most inversion height And there are
examples of Jategaonkar embeddings of height one and two.
- If there is an embedding of the free algebra on two generators of
then there exists an embedding of the free algebra on
an infinite number of generators of inversion height
- Let be the free algebra or the free group algebra on
generators. We use examples in to obtain embeddings of of inversion height or
- In a Jategaonkar embedding is never the universal field of fractions of
- joint work with D. Herbera