$\omega$-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.

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How to Cite
(1)
Romaniv, O.; Sagan, A. $\omega$-Euclidean Domain and Laurent Series. Carpathian Math. Publ. 2016, 8, 158-162.