### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 251-284 |

Number of pages | 34 |

Journal | Algebras and Representation Theory |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2003 |

### Keywords

- Almost split
- Approximation
- Artin algebra
- Contravariantly finite
- Covariantly finite
- Ext-injective
- Ext-projective
- Extension closed
- Module
- Prinjective
- Relatively projective
- Sequence
- Subcategory

### ASJC Scopus subject areas

- Mathematics(all)