{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T10:41:37Z","timestamp":1742640097987},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Algebra Appl."],"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p> An element [Formula: see text] in a ring [Formula: see text] is called clean if it is the sum of an idempotent [Formula: see text] and a unit [Formula: see text]. Such a clean decomposition [Formula: see text] is said to be strongly clean if [Formula: see text] and special clean if [Formula: see text]. In this paper, we prove that [Formula: see text] is Drazin invertible if and only if there exists an idempotent [Formula: see text] and a unit [Formula: see text] such that [Formula: see text] is both a strongly clean decomposition and a special clean decomposition, for some positive integer [Formula: see text]. Also, the existence of the Moore\u2013Penrose and group inverses is related to the existence of certain \u2217-clean decompositions. <\/jats:p>","DOI":"10.1142\/s0219498819501330","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T22:32:34Z","timestamp":1531434754000},"page":"1950133","source":"Crossref","is-referenced-by-count":2,"title":["Generalized inverses and their relations with clean decompositions"],"prefix":"10.1142","volume":"18","author":[{"given":"Huihui","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei 230009, P. R. 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