We discuss the problem of classification of indecomposable representations for extended Dynkin quivers of type 𝔼̃₈, with a fixed orientation. We describe a method for an explicit determination of all indecomposable preprojective and preinjective representations for those quivers over an arbitrary field and for all indecomposable representations in case the field is algebraically closed. This method uses tilting theory and results about indecomposable modules for a canonical algebra of type (5,3,2)...

We study whether the projective and injective properties of left $R$-modules can be implied to the special kind of left $R\left[x\right]$-modules, especially to the case of inverse polynomial modules and Laurent polynomial modules.