  Let $k$ be a field, and let $\Lambda$ be a finite dimensional $k$-algebra. We
prove that if $\Lambda$ is a self-injective algebra, then every finitely
generated $\Lambda$-module $V$ whose stable endomorphism ring is isomorphic to
$k$ has a universal deformation ring $R(\Lambda,V)$ which is a complete local
commutative Noetherian $k$-algebra with residue field $k$. If $\Lambda$ is also
a Frobenius algebra, we show that $R(\Lambda,V)$ is stable under taking
syzygies. We investigate a particular Frobenius algebra $\Lambda_0$ of dihedral
type, as introduced by Erdmann, and we determine $R(\Lambda_0,V)$ for every
finitely generated $\Lambda_0$-module $V$ whose stable endomorphism ring is
isomorphic to $k$.
