{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:52:05Z","timestamp":1776214325339,"version":"3.50.1"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,4,9]],"date-time":"2009-04-09T00:00:00Z","timestamp":1239235200000},"content-version":"unspecified","delay-in-days":2624,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Aust. Math. Soc."],"published-print":{"date-parts":[[2002,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we define and study a generalized Drazin inverse <jats:italic>x<\/jats:italic><jats:sup>D<\/jats:sup> for ring elements <jats:italic>x<\/jats:italic>, and give a characterization of elements <jats:italic>a<\/jats:italic>, <jats:italic>b<\/jats:italic> for which <jats:italic>aa<\/jats:italic><jats:sup>D<\/jats:sup> = <jats:italic>bb<\/jats:italic><jats:sup>D<\/jats:sup>. We apply our results to the study of EP elements in a ring with involution.<\/jats:p>","DOI":"10.1017\/s1446788700003657","type":"journal-article","created":{"date-parts":[[2009,4,14]],"date-time":"2009-04-14T04:47:13Z","timestamp":1239684433000},"page":"137-152","source":"Crossref","is-referenced-by-count":144,"title":["Elements of rings with equal spectral idempotents"],"prefix":"10.1017","volume":"72","author":[{"given":"J. J.","family":"Koliha","sequence":"first","affiliation":[]},{"given":"Pedro","family":"Patricio","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,4,9]]},"reference":[{"key":"S1446788700003657_ref013","first-page":"197","article-title":"Continutiy of generalized inverse in Banach algebras","volume":"136","author":"Roch","year":"1999","journal-title":"Studia Math."},{"key":"S1446788700003657_ref011","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100030401"},{"key":"S1446788700003657_ref010","doi-asserted-by":"publisher","DOI":"10.4064\/sm-139-1-81-90"},{"key":"S1446788700003657_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(78)90029-0"},{"key":"S1446788700003657_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF00281485"},{"key":"S1446788700003657_ref004","volume-title":"Invertibility and singularity for bounded linear operators","author":"Harte","year":"1988"},{"key":"S1446788700003657_ref003","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1958.11991949"},{"key":"S1446788700003657_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(00)00101-4"},{"key":"S1446788700003657_ref001","volume-title":"Generalized inverses of linear transformations","author":"Campbell","year":"1991"},{"key":"S1446788700003657_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(81)90145-2"},{"key":"S1446788700003657_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500031803"},{"key":"S1446788700003657_ref009","first-page":"17","article-title":"The Drazin and Moore\u2013Penrose inverse in C*-algebra","volume":"99","author":"Koliha","year":"1999","journal-title":"Math. Proc. Roy. Irish Acad."},{"key":"S1446788700003657_ref005","first-page":"10","article-title":"On quasinilpotents in rings","volume":"1","author":"Harte","year":"1991","journal-title":"Panam. Math. J."}],"container-title":["Journal of the Australian Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1446788700003657","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T15:17:31Z","timestamp":1557242251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1446788700003657\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,2]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,2]]}},"alternative-id":["S1446788700003657"],"URL":"https:\/\/doi.org\/10.1017\/s1446788700003657","relation":{},"ISSN":["1446-7887","1446-8107"],"issn-type":[{"value":"1446-7887","type":"print"},{"value":"1446-8107","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,2]]}}}