  By a ring we always mean a commutative ring with identity. It is well known
that maximal spectrum of $C(X)$, $C^*(X)$ and any intermediate subrings between
$C(X)$ and $C^* (X)$ are homeomorphic and homeomorphic with $\beta X$, the
Stone-$\check{C}$ech compactification of $X$. In this paper we generalized
these results to an arbitrary ring by introducing a notion of dense subring. We
proved that if $A$ is completely normal and dense subring of $B$, then maximal
spectrum of $A$ and $B$ are homeomorphic and hence maximal spectrum of all
intermediate subrings between $A$ and $B$ where $A$ is dense, are homeomorphic.
We also proved that $A$ is dense subring of $B$ if and only if spectrum of $B$
is densely embedded in spectrum of $A$ and have further shown that if $A$ is
dense subring of $B$, any minimal prime ideal of $A$ is precisely of the form
$Q\cap A$ for some unique minimal prime ideal $Q$ of $B$. As a consequence, we
concluded that if $A$ is dense in $B$, minimal spectrum of $A$ and that of $B$
are homeomorphic. We also studied different properties of dense subrings of a
ring.
