{"paper":{"title":"The cotorsion pair generated by the Gorenstein projective modules and $\\lambda$-pure-injective modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RT","authors_text":"Jan \\v{S}aroch, Manuel Cort\\'es-Izurdiaga","submitted_at":"2021-04-17T17:53:54Z","abstract_excerpt":"We prove that, if $\\textrm{GProj}$ is the class of all Gorenstein projective modules over a ring $R$, then $\\mathfrak{GP}=(\\textrm{GProj},\\textrm{GProj}^\\perp)$ is a cotorsion pair. Moreover, $\\mathfrak{GP}$ is complete when all projective modules are $\\lambda$-pure-injective for some infinite regular cardinal $\\lambda$ (in particular, if $R$ is right $\\Sigma$-pure-injective); the latter condition is shown to be consistent with the axioms of ZFC modulo the existence of strongly compact cardinals.\n  We also thoroughly study $\\lambda$-pure-injective modules for an arbitrary infinite regular card"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.08602","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.08602/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"}