Presentations of Monomial Algebras and Uniserial Modules

Abstract

Finite dimensional monomial algebras have naturally defined uniserial modules for each path in the quiver nonzero in the algebra. This observation is used to give a new characterization of monomial algebras and a necessary condition for an algebra to be 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 ⇒ monomial.”

Keywords:

• Constricted algebra
• Monomial algebra
• Uniserial module

Mathematics Subject Classification:

• 16G10
• 16G20

ACKNOWLEDGMENT

This work is part of the author's doctoral dissertation at the University of Ottawa under the supervision of Professor Walter D. Burgess. The author wishes to thank him for his helpful guidance and suggestions. The author would also like to thank the Department of Mathematics at the University of Ottawa for financial support.

Notes

Communicated by B. Huisgen-Zimmermann.