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 language||English (US)|
|Number of pages||19|
|Journal||Journal of Algebra|
|State||Published - Mar 1 2002|
- Almost split sequence
ASJC Scopus subject areas
- Algebra and Number Theory