# Algorithm of divisibility over generalizations of polynomial rings

- Written by Andrij Sagan
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*Department of Algebra and Logic** Faculty of Mechanics and Mathematics** Ivan Franko National University of L'vivemail: andrij.sagan at gmail.com*

**Abstract:**

*We will prove that a integral domain R is an ω-Euclidean ring if and only if a ring of formal Laurent series R[[X, X ^{-1}]] is an ω-Euclidean ring. *

*Finally, we will prove that a domain R is ω -Euclidean if and only if R<X> is ω-Euclidean domain. Also, we show that R is a Bezout domain if and only if R(X) is a ring of elementary reduction matrices.*

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