Bezout Rings of Stable Range 1.5

  • V. P. Shchedrik

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.
Published
25.06.2015
How to Cite
Shchedrik, V. P. “Bezout Rings of Stable Range 1.5”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 6, June 2015, pp. 849–860, http://umj.imath.kiev.ua/index.php/umj/article/view/2027.
Section
Research articles