$\omega$-Euclidean domain and Laurent series

O. M. Romaniv, A. V. Sagan


It is proved that a commutative domain $R$ is $\omega$-Euclidean if and only if the ring of formal Laurent series over $R$ is $\omega$-Euclidean domain. It is also proved that every singular matrice over ring of formal Laurent series $R_{X}$ are products of idempotent matrices if $R$ is $\omega$-Euclidean domain.


$\omega$-Euclidean domain, formal Laurent series, idempotent matrices

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