# A stable range of class full matrices over elementary divisor ring

- Written by B. Kuznitska
- Be the first to comment!

*Department of Algebra and Logic** Faculty of Mechanics and Mathematics** Ivan Franko National University of L'viv*

** **

Abstract:

**Theorem 1.** *Let R be a commutative Bezout ring a stable range 2. Let A, B∈ F(R _{2}) be such that AR_{2}+BR_{2}=R_{2}, moreover, the matrix B admits a diagonal reduction. Then there exists a full matrix T∈ F(R_{2}) such that A+BT is an invertible matrix. *

**Theorem 2.** *Let R be a commutative elementary divisor ring. If A, B∈ F(R _{2}) and AR_{2}+BR_{2}=R_{2}, then there exists full matrix T∈ F(R_{2}) such that A+BT is an invertible matrix.*

* *

* *

## Коментарі (0)