Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
email: andrij.sagan at gmail.com
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.