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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03243 |
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Table of Contents:
- 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.