{"paper":{"title":"Injective DG-modules over non-positive DG-rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.KT"],"primary_cat":"math.RA","authors_text":"Liran Shaul","submitted_at":"2017-09-05T16:25:21Z","abstract_excerpt":"Let $A$ be an associative non-positive differential graded ring. In this paper we make a detailed study of a category $\\operatorname{\\mathsf{Inj}}(A)$ of left DG-modules over $A$ which generalizes the category of injective modules over a ring. We give many characterizations of this category, generalizing the theory of injective modules, and prove a derived version of the Bass-Papp theorem: the category $\\operatorname{\\mathsf{Inj}}(A)$ is closed in the derived category $\\operatorname{\\mathsf{D}}(A)$ under arbitrary direct sums if and only if the ring $\\mathrm{H}^0(A)$ is left noetherian and for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01479","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}