The first Brauer-Thrall conjecture for extriangulated length categories

Le résumé fourni par la source

Let $(\mathcal{A},Θ)$ be a length category. We introduce the notation of Gabriel-Roiter measure with respect to $Θ$ and extend Gabriel's main property to this setting. Using this measure, when $(\mathcal{A},Θ)$ satisfies some technical conditions, we prove that $\mathcal{A}$ has an infinite number of pairwise nonisomorphic indecomposable objects if and only if it has indecomposable objects of arbitrarily large length. That is, the first Brauer-Thrall conjecture holds.

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