  In this paper, at first, we show that for a ramified regular local ring $S$,
which is an Eisenstein extension of an unramified regular local ring $R$, when
an ideal $I$ of $S$ is extended from an ideal $J$ of $R$, the punctured
spectrum of $R/J$ is connected if that of $S/JS$ is connected. Using this, we
extend the result of SVT to complete ramified regular local ring only for the
extended ideals. If the punctured spectrum of $S/JS$ is disconnected then that
of $R/J$ is also disconnected when every minimal primes $\p$ of $J$, $R/\p$ is
normal. Under this situation we prove that both of them have the same number of
connected components. Finally, we show that for both unramified and ramified
regular local rings (for extended ideal via Eisenstein extension), two top-most
local cohomology modules satisfy the Conjecture 1 of \cite{L-Y}, although the
conjecture is false in general.
