  In this article, we continue our study of the ring of Baire one functions on
a topological space $(X,\tau)$, denoted by $B_1(X)$ and extend the well known
M. H. Stones's theorem from $C(X)$ to $B_1(X)$. Introducing the structure space
of $B_1(X)$, an analogue of Gelfand Kolmogoroff theorem is established. It is
observed that $(X,\tau)$ may not be embedded inside the structure space of
$B_1(X)$. This observation inspired us to introduce a weaker form of embedding
and show that in case $X$ is a $T_4$ space, $X$ is weakly embedded as a dense
subspace, in the structure space of $B_1(X)$. It is further established that
the ring $B_1^{*}(X)$ of all bounded Baire one functions is a C-type ring and
also, the structure space of $B_1^{*}(X)$ is homeomorphic to the structure
space of $B_1(X)$. Introducing a finer topology $\sigma$ than the original
$T_4$ topology $\tau$ on $X$, it is proved that $B_1(X)$ contains free
(maximal) ideals if $\sigma$ is strictly finer than $\tau$. It is also proved
that $\tau = \sigma$ if and only if $B_1(X) = C(X)$. Moreover, in the class of
all perfectly normal $T_1$ spaces, $B_1(X) = C(X)$ is equivalent to the
discreteness of the space $X$.
