The Kaplansky condition and rings of almost stable range 1

We present some variants of the Kaplansky condition for a K-Hermite ring R to be an elementary divisor ring. For example, a commutative K-Hermite ring R is an EDR iff for any elements x,y, z Ie{cyrillic, ukrainian} R such that (x, y) = R there exists an element λ Ie{cyrillic, ukrainian} R such that x + λy = uv, where (u,z) = (v, 1 - z) = R. We present an example of a Bezout domain that is an elementary divisor ring but does not have almost stable range 1, thus answering a question of Warren Wm. McGovern.