Web Modules and Applications Original Research Article

If k is a field and Q′ is a finite connected quiver without oriented cycles, its k-proper web module is the representation with a k at each vertex and an identity map at each arrow. Given a k-algebra Λ of the form kQ/I, the Λ-web modules are the ones induced by proper web modules and certain functors F: kQ′ → Λ (which we call qfaithful). One of the main results is that web modules are indecomposable. An application is given to show that all indecomposable modules of certain biserial algebras are web modules.