Some properties of the symbol algebras

Abstract

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 $K=\mathbb{Q}(\epsilon ),{\epsilon }^3=1,\epsilon \ne 1.$

This paper was accepted to publish in Carpathian Journal of Mathematics