  In this article we study a class of orders called {\it monomial orders} in a
central simple algebra over a non-Archimedean local field. Monomial orders are
easily represented and they may be also viewed as a direct generalization of
Eichler orders in quaternion algebras. A criterion for monomial orders to be
Gorenstein or to be Bass is given. It is shown that a monomial order is Bass if
and only if it is either a hereditary or an Eichler order of period two.
