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

$\omega$-Euclidean domain and skew Laurent series rings