{"paper":{"title":"The core and dual core inverses of morphisms with kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dingguo Wang, Jianlong Chen, Mengmeng Zhou, Tingting Li","submitted_at":"2018-04-24T02:46:23Z","abstract_excerpt":"Let $\\mathscr{C}$ be an additive category with an involution $\\ast$. Suppose that $\\varphi : X \\rightarrow X$ is a morphism with kernel $\\kappa : K \\rightarrow X$ in $\\mathscr{C}$, then $\\varphi$ is core invertible if and only if $\\varphi$ has a cokernel $\\lambda: X \\rightarrow L$ and both $\\kappa\\lambda$ and $\\varphi^{\\ast}\\varphi^3+\\kappa^{\\ast}\\kappa$ are invertible. In this case, we give the representation of the core inverse of $\\varphi$. We also give the corresponding result about dual core inverse."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08820","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"}