  We describe of all finite dimensional uniserial representations of a
commutative associative (resp. abelian Lie) algebra over a perfect (resp.
sufficiently large perfect) field. In the Lie case the size of the field
depends on the answer to following question, considered and solved in this
paper. Let $K/F$ be a finite separable field extension and let $x,y\in K$. When
is $F[x,y]=F[\alpha x+\beta y]$ for some non-zero elements $\alpha,\beta\in F$?
