2017
Том 69
№ 6

All Issues

Bezout Rings of Stable Range 1.5

Shchedrik V. P.


Abstract

A ring $R$ has a stable range 1.5 if, for every triple of left relatively prime nonzero elements $a, b$ and $c$ in $R$, there exists $r$ such that the elements $a+br$ and $c$ are left relatively prime. Let $R$ be a commutative Bezout domain. We prove that the matrix ring $M_2 (R)$ has the stable range 1.5 if and only if the ring $R$ has the same stable range.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 6, pp 960-974.

Citation Example: Shchedrik V. P. Bezout Rings of Stable Range 1.5 // Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 849–860.