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

Mark Kleiner, Efren Perez

Research output: Contribution to journalArticle

6 Scopus citations

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 languageEnglish (US)
Pages (from-to)251-284
Number of pages34
JournalAlgebras and Representation Theory
Volume6
Issue number3
DOIs
StatePublished - 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)

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