The Almost Split Sequences for Trivial Extensions of Hereditary Algebras

Abstract

Let $A$ be a basic hereditary artin algebra and $R = A \ltimes Q$ be the trivial extension of $A$ by its minimal injective cogenerator $Q$. We construct some right (left) almost split morphisms and irreducible morphisms in mod$R$ through the corresponding morphisms in mod$A$. Furthermore, we can determine its almost split sequences in mod$R$.