Artin in his book, Geometric Algebra, says the connection between the left
degree and right degree of a skew-field extension is unknown.
Since I'm not an expert, I was wondering if someone knew the answer to this question. The book is rather old and there must have been some developments since that time. 



Left vs right degree of skew-field extensions
Anything that might happen does happen.


In


*Schofield, A. H.*, [**Artin’s problem for skew field extensions**](http://dx.doi.org/10.1017/S0305004100062538), Math. Proc. Camb. Philos. Soc. 97, 1-6 (1985). [ZBL0574.16008](https://zbmath.org/?q=an:0574.16008).


it is shown that for any integers $m,n>1$ there is a skew field extension with left degree $m$ and right degree $n$.


Cohn had previously proved the corresponding fact for an arbitrary pair of cardinals (greater than $1$) under the assumption that at least one is infinite. 


