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"I liked the algebraic way of looking at things.
I’m additionally fascinated when the algebraic method is applied to infinite objects”.

Irwing Kaplansky

Algorithm of divisibility over generalizations of polynomial rings

 

Andrij Sagan

Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
email: 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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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at franko.lviv.ua

Scientific seminar, Aprill, 2015