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Almost Split Sequences whose Middle Term has at most Two Indecomposable Summands

Published online by Cambridge University Press:  20 November 2018

M. Auslander
Affiliation:
Brandeis University, Waltham, Massachusetts
R. Bautista
Affiliation:
University of Mexico, Mexico
M. I. Platzeck
Affiliation:
University of Bahiá Blanca, Argentina
I. Reiten
Affiliation:
University of Trondheim, Norway
S. O. Smalø
Affiliation:
University of Trondheim, Norway
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Let Λ be an artin algebra, and denote by mod Λ the category of finitely generated Λ-modules. All modules we consider are finitely generated.

We recall from [6] that a nonsplit exact sequence in mod A is said to be almost split if A and C are indecomposable, and given a map h: XC which is not an isomorphism and with X indecomposable, there is some t: XB such that gt = h.

Almost split sequences have turned out to be useful in the study of representation theory of artin algebras. Given a nonprojective indecomposable Λ-module C (or an indecomposable noninjective Λ-module A), we know that

there exists a unique almost split sequence [6, Proposition 4.3], [5, Section 3].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1979

References

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