{"paper":{"title":"The Schr\\\"{o}der-Bernstein problem for Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ashish K. Srivastava, Berke Kalebo\\~gaz, Pedro A. Guil Asensio","submitted_at":"2017-03-14T22:33:47Z","abstract_excerpt":"In this paper we study the Schr\\\"{o}der-Bernstein problem for modules. We obtain a positive solution for the Schr\\\"{o}der-Bernstein problem for modules invariant under endomorphisms of their general envelopes under some mild conditions that are always satisfied, for example, in the case of injective, pure-injective or cotorsion envelopes. In the particular cases of injective envelopes and pure-injective envelopes, we are able to extend it further and we show that the Schr\\\"{o}der-Bernstein problem has a positive solution even for modules that are invariant only under automorphisms of their inj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04787","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"}