  Let $R$ be the associative $k$-algebra generated by two elements $x$ and $y$
with defining relation $yx=1$. A complete description of simple modules over
$R$ is obtained by using the results of Irving and Gerritzen. We examine the
short exact sequence $0\rightarrow U\rightarrow E \rightarrow V\rightarrow 0$,
where $U$ and $V$ are simple $R$-modules. It shows that nonsplit extension only
occurs when both $U$ and $V$ are one-dimensional, or, under certain condition,
$U$ is infinite-dimensional and $V$ is one-dimensional.
