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Almost split sequences for non-regular modules

S. Liu — 1993

Fundamenta Mathematicae

Let A be an Artin algebra and let $0 \to X \to \oplus_{i = 1}^{r} Y_{i} \to Z \to 0$ be an almost split sequence of A-modules with the $Y_{i}$ indecomposable. Suppose that X has a projective predecessor and Z has an injective successor in the Auslander-Reiten quiver $Γ_{A}$ of A. Then r ≤ 4, and r = 4 implies that one of the $Y_{i}$ is projective-injective. Moreover, if $X \to \oplus_{j = 1}^{t} Y_{j}$ is a source map with the $Y_{j}$ indecomposable and X on an oriented cycle in $Γ_{A}$ , then t ≤ 4 and at most three of the $Y_{j}$ are not projective. The dual statement for a sink map holds. Finally, if an arrow...

Invariant Means on a Locally Compact Group.

T.-s. Liu; Arnoud van Rooij — 1974

Monatshefte für Mathematik

On a family of weighted spaces

R. H. Fischer; Turan A. Gürkanli; T. S. Liu — 1996

Mathematica Slovaca

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