{"paper":{"title":"Specifying The Auslander transpose in submodule category and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Abdolnaser Bahlekeh, Ali Mahin Fallah, Shokrollah Salarian","submitted_at":"2018-08-22T18:21:32Z","abstract_excerpt":"Let $(R, \\m)$ be a $d$-dimensional commutative noetherian local ring. Let $\\M$ denote the morphism category of finitely generated $R$-modules and let $\\Sc$ be the submodule category of $\\M$. In this paper, we specify the Auslander transpose in submodule category $\\Sc$. It will turn out that the Auslander transpose in this category can be described explicitly within ${\\rm mod}R$, the category of finitely generated $R$-modules. This result is exploited to study the linkage theory as well as the Auslander-Reiten theory in $\\Sc$. Indeed, a characterization of horizontally linked morphisms in terms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07508","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"}