{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T10:54:22Z","timestamp":1742640862375},"reference-count":0,"publisher":"National Library of Serbia","issue":"12","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Filomat"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>Let R be an associative ring with unity 1 and let a,d ? R. An element a ? R\n   is called invertible along d if there exists unique a??d such that a??dad = d\n   = daa??d and a??d ? dR ? Rd (see [6, Definition 4]). In this note, we present\n   new characterizations for the existence of akd by clean decompositions of ad\n   and da. As applications, existence criteria for the Drazin inverse and the\n   group inverse are given.<\/jats:p>","DOI":"10.2298\/fil1812285z","type":"journal-article","created":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T13:22:47Z","timestamp":1555939367000},"page":"4285-4290","source":"Crossref","is-referenced-by-count":2,"title":["A note on clean elements and inverses along an element"],"prefix":"10.2298","volume":"32","author":[{"given":"Huihui","family":"Zhu","sequence":"first","affiliation":[{"name":"nema"}]},{"given":"Pedro","family":"Patr\u00edcio","sequence":"additional","affiliation":[{"name":"nema"}]}],"member":"1078","container-title":["Filomat"],"original-title":[],"language":"en","deposited":{"date-parts":[[2023,5,29]],"date-time":"2023-05-29T08:08:58Z","timestamp":1685347738000},"score":1,"resource":{"primary":{"URL":"https:\/\/doiserbia.nb.rs\/Article.aspx?ID=0354-51801812285Z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":0,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2018]]}},"URL":"https:\/\/doi.org\/10.2298\/fil1812285z","relation":{},"ISSN":["0354-5180","2406-0933"],"issn-type":[{"value":"0354-5180","type":"print"},{"value":"2406-0933","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]}}}