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

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