The kernel of an irreducible map-Reference-Cited by-同舟云学术

The kernel of an irreducible map

Published:1994 Issue:1 Volume:121 Page:57-66
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Krause Henning

Abstract

Let 0 → A → B → g C → 0 0 \to A \to B\xrightarrow {g}C \to 0 be a short exact sequence in the category of finitely generated modules over an artin algebra. Suppose also that the map g is irreducible. Following a conjecture of Brenner, we discuss the property of the indecomposable module A to be the starting term of an almost split sequence with indecomposable middle term.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1994-121-01/S0002-9939-1994-1181169-8/S0002-9939-1994-1181169-8.pdf

Reference7 articles.

1. Functors and morphisms determined by objects;Auslander, Maurice,1978

2. Representation theory of Artin algebras. III. Almost split sequences;Auslander, Maurice;Comm. Algebra,1975

3. Representation theory of Artin algebras. IV. Invariants given by almost split sequences;Auslander, Maurice;Comm. Algebra,1977

4. S. Brenner, On kernels of irreducible maps, preprint, 1991.

5. Auslander-Reiten sequences with few middle terms and applications to string algebras;Butler, M. C. R.;Comm. Algebra,1987

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