{"paper":{"title":"Indecomposability of graded modules over a graded ring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Mitsuyasu Hashimoto, Yuntian Yang","submitted_at":"2023-06-26T08:56:37Z","abstract_excerpt":"Let $R=\\bigoplus_{i\\geq 0}R_i$ be a Noetherian commutative non-negatively graded ring such that $(R_0,\\mathfrak{m}_0)$ is a Henselian local ring. Let $\\mathfrak{m}$ be its unique graded maximal ideal $\\mathfrak{m}_0+\\bigoplus_{i>0}R_i$. Let $T$ be a module-finite (non-commutative) graded $R$-algebra. Let $T\\mathop{\\mathrm{grmod}}$ denote the category of finite graded left $T$-modules, and $M\\in T\\mathop{\\mathrm{grmod}}$. Then the following are equivalent: (1) $\\hat M$ is an indecomposable $\\hat T$-module, where $\\widehat{(-)}$ denotes the $\\mathfrak{m}$-adic completion; (2) $M_{\\mathfrak{m}}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.14523","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.14523/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}