Bezout rings of stable ranк 1.5 and the decomposition of a complete linear group into its multiple subgroups

• Date: 2017
• Main Authors: Shchedrik, V. P., Щедрик, В. П.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1680
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

A ring $R$ is called a ring of stable rank 1.5 if, for any triple $a, b, c \in R, c \not = 0$, such that $aR + bR + cR = R$, there exists $r \in R$ such that $(a + br)R + cR = R$. It is proved that a commutative Bezout domain has a stable rank 1.5 if and only if every invertible matrix $A$ can be...