{"paper":{"title":"Some New Results on Pseudo n-Strong Drazin Inverses in Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Jian Cui, Peter Danchev, Yuedi Zeng","submitted_at":"2023-12-04T21:21:24Z","abstract_excerpt":"In this paper, we give a further study in-depth of the pseudo $n$-strong Drazin inverses in an associative unital ring $R$. The characterizations of elements $a,b\\in R$ for which $aa^{\\tiny{\\textcircled{\\qihao D}}}=bb^{\\tiny{\\textcircled{\\qihao D}}}$ are provided, and some new equivalent conditions on pseudo $n$-strong Drazin inverses are obtained. In particular, we show that an element $a\\in R$ is pseudo $n$-strong Drazin invertible if, and only if, $a$ is $p$-Drazin invertible and $a-a^{n+1}\\in \\sqrt{J(R)}$ if, and only if, there exists $e^2=e\\in {\\rm comm}^2(a)$ such that $ae\\in \\sqrt{J(R)}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.02347","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.02347/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"}