Presentations of monomial algebras and uniserial modules

Finite dimensional monomial algebras have naturally defined uniserial modules for each path in the quiver nonzero in tire algebra. This observation is used to give a new characterization of monomial algebras and a necessary condition for an algebra to he isomorphic to a monomial algebra. The characterization of these latter algebras due to Bardzell and Green is revisited using uniserial modules. A class of algebras, strictly larger than previously studied ones, is found in which "isomorphic to a monomial algebra double right arrow monomial."