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.
- Bezout rings of stable range 2 and square stable range 1
- A pseudo-prime elements of a commutative domain
- A pseudo-irreducible elements of a commutative domain
- Commutative Bezout domains in which any nonzero prime ideal is contained in a finite set of maximal ideals
- On stable range of matrix rings over commutative principal ideal rings