Title of article :
Almost Split Sequences for Comodules
Author/Authors :
William Chin، نويسنده , , Mark Kleiner ، نويسنده , , Declan Quinn، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2002
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.
Keywords :
Coalgebra , Comodule , almost split sequence , transpose , semiperfect
Journal title :
Journal of Algebra
Journal title :
Journal of Algebra