The kernel of an irreducible map

Author:
Henning Krause

Journal:
Proc. Amer. Math. Soc. **121** (1994), 57-66

MSC:
Primary 16G70

MathSciNet review:
1181169

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Abstract: Let 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.

**[A]**Maurice Auslander,*Functors and morphisms determined by objects*, Representation theory of algebras (Proc. Conf., Temple Univ., Philadelphia, Pa., 1976) Dekker, New York, 1978, pp. 1–244. Lecture Notes in Pure Appl. Math., Vol. 37. MR**0480688****[AR1]**Maurice Auslander and Idun Reiten,*Representation theory of Artin algebras. III. Almost split sequences*, Comm. Algebra**3**(1975), 239–294. MR**0379599****[AR2]**Maurice Auslander and Idun Reiten,*Representation theory of Artin algebras. IV. Invariants given by almost split sequences*, Comm. Algebra**5**(1977), no. 5, 443–518. MR**0439881****[B]**S. Brenner,*On kernels of irreducible maps*, preprint, 1991.**[BR]**M. C. R. Butler and Claus Michael Ringel,*Auslander-Reiten sequences with few middle terms and applications to string algebras*, Comm. Algebra**15**(1987), no. 1-2, 145–179. MR**876976**, 10.1080/00927878708823416**[K]**Henning Krause,*On the number of almost split sequences with indecomposable middle term*, Bull. London Math. Soc.**26**(1994), no. 5, 422–426. MR**1308357**, 10.1112/blms/26.5.422**[M]**Roberto Martínez-Villa,*Almost projective modules and almost split sequences with indecomposable middle term*, Comm. Algebra**8**(1980), no. 12, 1123–1150. MR**579792**, 10.1080/00927878008822512

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1181169-8

Article copyright:
© Copyright 1994
American Mathematical Society