Abstract
Coverings in representation theory have been successfully used by: BongartzGabriel [2], Gabriel [3], Green [4], Riedtman [6, 7]. Of particular importance is the study of the relations between the coverings of the Auslander-Reiten quiver and the ordinary quiver. In this direction P. Gabriel posed, in the Third International Conference on Representations of Algebras, Puebla M6xico, 1980, the following conjecture: "Let g be an automorphism of an algebra A of finite representation type. For each right module M, denote by M g the A-module with underlying group M and scalar multiplication (m, 2 )~mgl (2 ) . If Sgq~S for each simple S, then M g q~ M for each indecomposable M". The aim of this note is to give a short proof of this statement. The conjecture is not true for algebras of infinite representation type. Con-
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