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

Oleh Romaniv; Andrij Sagan

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arXiv · 1707.02734

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

Oleh Romaniv·Andrij Sagan

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Abstract

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.

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Oleh Romaniv, Andrij Sagan. 2017-07-10. $\omega$-Euclidean domain and skew Laurent series rings. https://arxiv.org/abs/1707.02734

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