**Javier Sánchez Serdà ^{1}**

Università degli Studi dell'Insubria,

Universitat Autònoma de Barcelona

Universitat Autònoma de Barcelona

Suppose we have a domain embedded in a division ring . We
define inductively:

, and for

.

Then
is
the smallest division ring that contains inside .
We define
, the *inversion height* of inside as if there is
no
such that is a division ring.
Otherwise,

Let be a commutative field. Suppose
is a ring
homomorphism which is not onto. Let
and
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*.

We prove:

- 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
height
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

- ...à
^{1} - joint work with D. Herbera

2005-05-23