  In this paper we proved that if $R$ is right $\omega$-Euclidean domain, then
skew Laurent formal series ring is right $\omega$-Euclidean domain. We also
showed that if $R$ is a right $\omega$-Euclidean domain with multiplicative
norm, then skew Laurent formal series ring is a right principal ideal domain.
In addition, we proved that if $R$ is a noncommutative $\omega$-Euclidean
domain with a multiplicative norm, then $R$ and skew Laurent formal series ring
is a ring with elementary reduction of matrices.
