The kernel of an irreducible map

Krause, Henning

doi:10.1090/S0002-9939-1994-1181169-8

The kernel of an irreducible map
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Proc. Amer. Math. Soc. 121 (1994), 57-66 Request permission

Abstract:

Let $0 \to A \to B\xrightarrow {g}C \to 0$ 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.

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