  Let $\mathcal{E}_1(M)^+$ be the local ring of germs at 0 of functions
belonging to a given Denjoy-Carleman quasianalytic class in a neighborhood of 0
in $[0,+\infty[$. We show that the ring $\mathcal{E}_1(M)^+$ contains elements
that cannot be extended quasianalytically in a neighborhood of 0 in
$\mathbb{R}$, unless it coincides with the ring of real-analytic germs.
