$\omega$-Euclidean domain and Laurent series

O.M. Romaniv; A.V. Sagan

doi:10.15330/cmp.8.1.158-162

$\omega$ -Euclidean domain and Laurent series

Authors

O.M. Romaniv Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine https://orcid.org/0000-0002-8022-7859
A.V. Sagan Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine

https://doi.org/10.15330/cmp.8.1.158-162

Keywords:

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

Published online: 2016-06-30

Abstract

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.