  In this paper, we obtain some properties of the symbol algebras, starting
from their connections with the quaternion and cyclic algebras over a field
$K_{p},$% where $K$ is an algebraic number field, $p$ is a prime in $K$ and
$K_{p}$ is the completion of $K$ with respect to $p-$ adic valuation, in the
case when $K=\Bbb{Q}(\varepsilon), \varepsilon ^{3}=1,\varepsilon \neq 1.$
