Computation of Almost Split Sequences with Applications to Relatively Projective and Prinjective Modules

Let Λ be an Artin algebra, let mod Λ be the category of finitely generated A-modules, and let script A sign ⊂ mod Λ be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module C ∈ script A sign, we compute the almost split sequence 0 → A → B → C → 0 in script A signA from the almost split sequence 0 → D Tr C → E → C → 0 in mod A. Since the computation is particularly simple if the minimal right script A sign-approximation of D Tr C is indecomposable for all indecomposable and not Ext-projective C ∈ A, we manufacture subcategories script A sign with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules.