Full embeddings of almost split sequences over split-by-nilpotent extensions
Volume 81 / 1999
Colloquium Mathematicum 81 (1999), 21-31
DOI: 10.4064/cm-81-1-21-31
Abstract
Let R be a split extension of an artin algebra A by a nilpotent bimodule $_A Q_A$, and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if $Hom_A (Q, τ_A M)$ = 0 and $M ⊗ _A Q = 0$.
