Javier Sánchez Serdà1
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: