{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T18:25:13Z","timestamp":1770488713876,"version":"3.49.0"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2017,9,23]],"date-time":"2017-09-23T00:00:00Z","timestamp":1506124800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11371089"],"award-info":[{"award-number":["11371089"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the Natural Science Foundation of Jiangsu Province","award":["BK20141327"],"award-info":[{"award-number":["BK20141327"]}]},{"name":"the Fundamental Research Funds for the Central Universities and the Foundation of Graduate Innovation Program of Jiangsu Province","award":["KYZZ15-0049"],"award-info":[{"award-number":["KYZZ15-0049"]}]},{"name":"the Scientific Innovation Research of College Graduates in Jiangsu Province","award":["CXLX13-072"],"award-info":[{"award-number":["CXLX13-072"]}]},{"name":"the Scientific Research Foundation of Graduate School of Southeast University and the Fundamental Research Funds for the Central Universities","award":["22420135011"],"award-info":[{"award-number":["22420135011"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mediterr. J. Math."],"published-print":{"date-parts":[[2017,10]]},"DOI":"10.1007\/s00009-017-1017-4","type":"journal-article","created":{"date-parts":[[2017,9,23]],"date-time":"2017-09-23T08:17:53Z","timestamp":1506154673000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["The One-Sided Inverse Along an Element in Semigroups and Rings"],"prefix":"10.1007","volume":"14","author":[{"given":"Jianlong","family":"Chen","sequence":"first","affiliation":[]},{"given":"Honglin","family":"Zou","sequence":"additional","affiliation":[]},{"given":"Huihui","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Pedro","family":"Patr\u00edcio","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,9,23]]},"reference":[{"key":"1017_CR1","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1080\/03081080902778222","volume":"58","author":"OM Baksalary","year":"2010","unstructured":"Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58, 681\u2013697 (2010)","journal-title":"Linear Multilinear Algebra"},{"key":"1017_CR2","doi-asserted-by":"crossref","first-page":"572","DOI":"10.13001\/1081-3810.3113","volume":"31","author":"J Ben\u00edtez","year":"2016","unstructured":"Ben\u00edtez, J., Boasso, E.: The inverse along an element in rings. Electron. J. Linear Algebra 31, 572\u2013592 (2016)","journal-title":"Electron. J. Linear Algebra"},{"key":"1017_CR3","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1080\/03081087.2016.1183559","volume":"65","author":"J Ben\u00edtez","year":"2017","unstructured":"Ben\u00edtez, J., Boasso, E.: The inverse along an element in rings with an involution, Banach algebras and \n                        $$C^{\\ast }$$\n                        \n                            \n                                            \n                                \n                                    C\n                                    *\n                                \n                            \n                        \n                    -algebras. Linear Multilinear Algebra 65, 284\u2013299 (2017)","journal-title":"Linear Multilinear Algebra"},{"key":"1017_CR4","doi-asserted-by":"publisher","unstructured":"Chen, J.L., Zhu, H.H., Patr\u00edcio, P., Zhang, Y.L.: Characterizations and representations of core and dual core inverses. Can. Math. Bull. doi:\n                        10.4153\/CMB-2016-045-7","DOI":"10.4153\/CMB-2016-045-7"},{"key":"1017_CR5","doi-asserted-by":"crossref","first-page":"506","DOI":"10.2307\/2308576","volume":"65","author":"MP Drazin","year":"1958","unstructured":"Drazin, M.P.: Pseudo-inverses in associative rings and semigroups. Am. Math. Mon. 65, 506\u2013514 (1958)","journal-title":"Am. Math. Mon."},{"key":"1017_CR6","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2307\/1969317","volume":"54","author":"JA Green","year":"1951","unstructured":"Green, J.A.: On the structure of semigroups. Ann. Math. 54, 163\u2013172 (1951)","journal-title":"Ann. Math."},{"key":"1017_CR7","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF00281485","volume":"61","author":"RE Hartwig","year":"1976","unstructured":"Hartwig, R.E.: Block generalized inverses. Arch. Ration. Mech. Anal. 61, 197\u2013251 (1976)","journal-title":"Arch. Ration. Mech. Anal."},{"key":"1017_CR8","doi-asserted-by":"crossref","first-page":"449","DOI":"10.2140\/pjm.1977.71.449","volume":"71","author":"RE Hartwig","year":"1977","unstructured":"Hartwig, R.E., Luh, J.: A note on the group structure of unit regular ring elements. Pac. J. Math. 71, 449\u2013461 (1977)","journal-title":"Pac. J. Math."},{"key":"1017_CR9","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1017\/S1446788700003657","volume":"72","author":"JJ Koliha","year":"2002","unstructured":"Koliha, J.J., Patr\u00edcio, P.: Elements of rings with equal spectral idempotents. J. Austral. Math. Soc. 72, 137\u2013152 (2002)","journal-title":"J. Austral. Math. Soc."},{"key":"1017_CR10","doi-asserted-by":"crossref","unstructured":"Lam, T.Y.: A First Course in Noncommutative Rings, Grad. Text in Math., vol. 131, 2nd edn. Springer, Berlin (2001)","DOI":"10.1007\/978-1-4419-8616-0"},{"key":"1017_CR11","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1016\/j.laa.2010.11.045","volume":"434","author":"X Mary","year":"2011","unstructured":"Mary, X.: On generalized inverses and Green\u2019s relations. Linear Algebra Appl. 434, 1836\u20131844 (2011)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"1017_CR12","first-page":"886","volume":"219","author":"X Mary","year":"2012","unstructured":"Mary, X., Patr\u00edcio, P.: The inverse along a lower triangular matrix. Appl. Math. Comput. 219(3), 886\u2013891 (2012)","journal-title":"Appl. Math. Comput."},{"key":"1017_CR13","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1080\/03081087.2012.731054","volume":"61","author":"X Mary","year":"2013","unstructured":"Mary, X., Patr\u00edcio, P.: Generalized inverses modulo \n                        $$\\cal{H}$$\n                        \n                            \n                                            \n                                H\n                            \n                        \n                     in semigroups and rings. Linear Multilinear Algebra 61, 1130\u20131135 (2013)","journal-title":"Linear Multilinear Algebra"},{"issue":"334","key":"1017_CR14","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/S0024-3795(01)00298-1","volume":"332","author":"P Patr\u00edcio","year":"2001","unstructured":"Patr\u00edcio, P.: The Moore\u2013Penrose inverse of von Neumann regular matrices over a ring. Linear Algebra Appl. 332(334), 469\u2013483 (2001)","journal-title":"Linear Algebra Appl."},{"key":"1017_CR15","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1017\/S0305004100030401","volume":"51","author":"R Penrose","year":"1955","unstructured":"Penrose, R.: A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51, 406\u2013413 (1955)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"1017_CR16","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.laa.2014.09.003","volume":"463","author":"DS Raki\u0107","year":"2014","unstructured":"Raki\u0107, D.S., Din\u010di\u0107, N.\u010c., Djordjevi\u0107, D.S.: Group, Moore\u2013Penrose, core and dual core inverse in rings with involution. Linear Algebra Appl. 463, 115\u2013133 (2014)","journal-title":"Linear Algebra Appl."},{"key":"1017_CR17","first-page":"231","volume":"1","author":"SZ Xu","year":"2017","unstructured":"Xu, S.Z., Chen, J.L., Zhang, X.X.: New characterizations for core inverses in rings with involution. Front. Math. China 1, 231\u2013246 (2017)","journal-title":"Front. Math. China"},{"key":"1017_CR18","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1080\/03081087.2015.1043716","volume":"64","author":"HH Zhu","year":"2016","unstructured":"Zhu, H.H., Chen, J.L., Patr\u00edcio, P.: Further results on the inverse along an element in semigroups and rings. Linear Multilinear Algebra 64, 393\u2013403 (2016)","journal-title":"Linear Multilinear Algebra"},{"key":"1017_CR19","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1080\/03081087.2016.1178209","volume":"65","author":"HH Zhu","year":"2017","unstructured":"Zhu, H.H., Chen, J.L., Patr\u00edcio, P.: Reverse order law for the inverse along an element. Linear Multilinear Algebra 65, 166\u2013177 (2017)","journal-title":"Linear Multilinear Algebra"},{"key":"1017_CR20","doi-asserted-by":"publisher","unstructured":"Zou, H.L., Chen, J.L., Li, T.T., Gao, Y.F.: Characterizations and representations of the inverse along an element. Bull. Malays. Math. Sci. Soc. doi:\n                        10.1007\/s40840-016-0430-3","DOI":"10.1007\/s40840-016-0430-3"}],"container-title":["Mediterranean Journal of Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00009-017-1017-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00009-017-1017-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00009-017-1017-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T02:41:30Z","timestamp":1508208090000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00009-017-1017-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,23]]},"references-count":20,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,10]]}},"alternative-id":["1017"],"URL":"https:\/\/doi.org\/10.1007\/s00009-017-1017-4","relation":{},"ISSN":["1660-5446","1660-5454"],"issn-type":[{"value":"1660-5446","type":"print"},{"value":"1660-5454","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,23]]},"article-number":"208"}}