Monomial, Gorenstein and Bass orders

Abstract

In this article we study a class of orders called 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.