{"paper":{"title":"On $L_{n}$-Injective Modules and $L_{n}$-Injective Dimensions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Fanggui Wang, Lei Qiao, Qing Li, Shiqi Xing, Tao Xiong","submitted_at":"2015-09-24T05:05:18Z","abstract_excerpt":"Let $R$ be a ring, and $n$ a fixed nonnegative integer. An $R$-module $W$ is called $L_{n}$-injective if ${\\rm Ext}_{R}^{1}(M,W)=0$ for any $R$-module $M$ with flat dimension at most $n$. In this paper, we prove first that ($\\mathcal{F}_{n},\\mathcal{L}_{n}$) is a complete hereditary cotorsion theory, where $\\mathcal{F}_n$ (resp. $\\mathcal{L}_n$) denotes the class of all $R$-modules with flat dimension at most $n$ (resp. $L_{n}$-injective $R$-modules). Then we introduce the $L_{n}$-injective dimension of a module and $L_n$-global dimension of a ring. Finally, over rings with weak global dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07235","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":""},"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"}