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