  In this paper we study the $R$-braces $(M,+,\circ)$ such that $M\cdot M$ is
cyclic, where $R$ is the ring of $p$-adic and $\cdot$ is the product of the
radical $R$-algebra associated to $M$. In particular, we give a classification
up to isomorphism in the torsion-free case and up to isoclinism in the torsion
case. More precisely, the isomorphism classes and the isoclinism classes of
such radical algebras are in correspondence with particular equivalence classes
of the bilinear forms defined starting from the products of the algebras.
