On indecomposable modules over directed algebras

Dräxler, Peter

doi:10.1090/S0002-9939-1991-1062830-X

On indecomposable modules over directed algebras
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Proc. Amer. Math. Soc. 112 (1991), 321-327 Request permission

Abstract:

Generalizing a result of Bongartz we show that any nonsimple indecomposable module over a finite-dimensional $k$-algebra $A$ is an extension of an indecomposable and a simple module provided $k$ is a field with more than two elements and $A$ is representation directed. Our proof is based on fibre sums over simple modules and some known classification results on socle projective modules over peak algebras. In case the global dimension of $A$ is at most 2 our methods also yield a description of the dimension vectors of the indecomposable $A$-modules by the roots of the associated quadratic form.

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On the exact representations of partially ordered sets of finite type

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