Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
Theorem 1. Let R be a commutative Bezout ring a stable range 2. Let A, B∈ F(R2) be such that AR2+BR2=R2, moreover, the matrix B admits a diagonal reduction. Then there exists a full matrix T∈ F(R2) such that A+BT is an invertible matrix.
Theorem 2. Let R be a commutative elementary divisor ring. If A, B∈ F(R2) and AR2+BR2=R2, then there exists full matrix T∈ F(R2) such that A+BT is an invertible matrix.