  In this paper we continue our study of modules satisfying the prime radical
condition ($\mathbb{P}$-radical modules), that was introduced in Part I (see
\cite{BS}). Let $R$ be a commutative ring with identity. The purpose of this
paper is to show that the theory of spectrum of $\mathbb{P}$-radical
$R$-modules (with the Zariski topology) resembles to that of rings. First, we
investigate the behavior of $\mathbb{P}$-radical modules under localization and
direct sums. Finally, we describe the construction of a structure sheaf on the
prime spectrum Spec$(M)$, which generalizes the classical structure sheaf of
the ring $R$ in Algebraic Geometry to the module $M$.
