Almost split sequences for comodules

William Chin, Mark Kleiner, Declan Quinn

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

Let Γ be a coalgebra over a field k. We introduce an operator Tr that takes a right quasi-finitely copresented Γ-comodule M to a left quasi-finitely copresented Γ-comodule Tr M. If M is indecomposable not injective and Tr M is finite-dimensional over K, we prove the existence of an almost split sequence 0 → M → E → DTr M → 0 in the category of all right Γ-comodules, where D = Homk( , k). If Γ is right semiperfect and the embedding of each simple right comodule S into its injective envelope I(S) has the property that the socle of I(S)/S is finite-dimensional, the above almost split sequence exists for each finite-dimensional M, and DTr M is also finite-dimensional.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalJournal of Algebra
Volume249
Issue number1
DOIs
StatePublished - Mar 1 2002

Keywords

  • Almost split sequence
  • Coalgebra
  • Comodule
  • Semiperfect
  • Transpose

ASJC Scopus subject areas

  • Algebra and Number Theory

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