We describe 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
 $K/F$  be a finite separable field extension and let   $x,\,y\,\in \,K$ . When is
 $x,\,y\,\in \,K$ . When is   $F\left[ x,\,y \right]\,=\,F\left[ \alpha x\,+\,\beta y \right]$  for some nonzero elements
 $F\left[ x,\,y \right]\,=\,F\left[ \alpha x\,+\,\beta y \right]$  for some nonzero elements   $\alpha ,\,\beta \,\in \,F?$
 $\alpha ,\,\beta \,\in \,F?$