by Kleiner, Mark; Perez, Efren

Let Λ be an Artin algebra, let modΛ be the category of finitely generated Λ-modules, and let A⊂modΛ be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module C∈A, we compute the almost split sequence 0→A→B→C→0 in A from the almost split sequence 0→D TrC→E→C→0 in modΛ. Since the computation is particularly simple if the minimal right A-approximation of D TrC is indecomposable for all indecomposable and not Ext-projective C∈A, we manufacture subcategories A 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.

DOI: 10.1023/A:1025182712207
Print publication date: 8/1/2003
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