Let
R
R
be a Cohen-Macaulay local ring with maximal ideal
m
m
and suppose that
dim
R
≥
2
\dim R \geq 2
. Then
R
R
is regular if (and only if) for any Buchsbaum
R
R
-module
M
M
and for any integer
i
,
i
≠
dim
R
M
i,i \ne {\dim _R}M
, the canonical map
Ext
R
i
(
R
/
m
,
M
)
→
H
m
i
(
M
)
:=
lim
→
n
E
x
t
R
i
(
R
/
m
n
,
M
)
{\text {Ext}}_R^i\left ( {R/m,M} \right ) \to H_m^i\left ( M \right ): = \lim _{\substack {\to \\n}} \mathrm {Ext}_R^i \left (R/m^n, M \right )
is surjective. The hypothesis that
R
R
is Cohen-Macaulay is not superfluous. Two examples are given.