Djordjević, Dragan S.; Wei, Yimin Outer generalized inverses in rings. (English) Zbl 1111.15007 Commun. Algebra 33, No. 9, 3051-3060 (2005). Summary: We formulate basic results on outer generalized inverses of elements in rings. We characterize elements which have the same idempotents related to their particular outer generalized inverses and investigate positive generalized inverses in \(C^*\)-algebras. Cited in 2 ReviewsCited in 36 Documents MSC: 15A09 Theory of matrix inversion and generalized inverses 16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) 46L05 General theory of \(C^*\)-algebras 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Keywords:rings; \(C^*\)-algebras Citations:Zbl 0963.15002; Zbl 1044.47010; Zbl 0981.47001; Zbl 0999.16025; Zbl 0994.15005; Zbl 0993.15003; Zbl 0986.65038 PDFBibTeX XMLCite \textit{D. S. Djordjević} and \textit{Y. Wei}, Commun. Algebra 33, No. 9, 3051--3060 (2005; Zbl 1111.15007) Full Text: DOI References: [1] Ben-Israel A., Generalized Inverses: Theory and Applications., 2. ed. (2003) [2] Bouldin R. H., Pitman Ser. Res. Notes in Math. 66 pp 233– (1982) [3] Caradus S. R., Generalized Inverses and Operator Theory (1978) · Zbl 0434.47003 [4] DOI: 10.1016/S0024-3795(00)00101-4 · Zbl 0963.15002 · doi:10.1016/S0024-3795(00)00101-4 [5] DOI: 10.1080/0003681021000004474a · Zbl 1044.47010 · doi:10.1080/0003681021000004474a [6] Djordjević D. S., Publ. Math. Debrecen 59 (1) pp 147– (2001) [7] DOI: 10.2307/2308576 · Zbl 0083.02901 · doi:10.2307/2308576 [8] Harte R. E., Panam. Math. J. 1 pp 10– (1991) [9] Harte R. E., Studia Math. 103 pp 71– (1992) [10] DOI: 10.1017/S0017089500031803 · Zbl 0897.47002 · doi:10.1017/S0017089500031803 [11] Koliha J. J., Math. Proc. Royal Irish Acad. 99 pp 17– (1999) [12] DOI: 10.1017/S1446788700003657 · Zbl 0999.16025 · doi:10.1017/S1446788700003657 [13] DOI: 10.1080/01630568708816235 · Zbl 0633.47001 · doi:10.1080/01630568708816235 [14] DOI: 10.1016/B978-0-12-514250-2.50005-6 · doi:10.1016/B978-0-12-514250-2.50005-6 [15] DOI: 10.1137/0148095 · Zbl 0661.15002 · doi:10.1137/0148095 [16] DOI: 10.1017/S0305004100030401 · doi:10.1017/S0305004100030401 [17] Stanimirović P. S., Acta Math. Hungar. 92 (1) pp 121– (2001) [18] DOI: 10.1016/S0377-0427(00)00710-X · Zbl 0993.15003 · doi:10.1016/S0377-0427(00)00710-X [19] DOI: 10.1080/00207160108805075 · Zbl 0986.65038 · doi:10.1080/00207160108805075 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.