{"paper":{"title":"New characterizations for core inverses in rings with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jianlong Chen, Sanzhang Xu, Xiaoxiang Zhang","submitted_at":"2015-12-26T04:47:08Z","abstract_excerpt":"The core inverse for a complex matrix was introduced by Baksalary and Trenkler. Raki\\'c, Din\\v{c}i\\'c and Djordjevi\\'c generalized the core inverse of a complex matrix to the case of an element in a ring. They also proved that the core inverse of an element in a ring can be characterized by five equations and every core invertible element is group invertible. It is natural to ask when a group invertible element is core invertible, in this paper, we will answer this question. We will use three equations to characterize the core inverse of an element. That is, let $a, b\\in R$, then $a\\in R^{\\tin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08073","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"}