Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter January 7, 2016

Weighted generalized Drazin inverse in rings

Dijana Mosić and Dragan S. Djordjević

Abstract

In this paper, we introduce and investigate the weighted generalized Drazin inverse in rings. We also introduce and investigate the weighted EP elements

MSC 2010: 16B99; 46H05; 47A05

Funding statement: The authors are supported by the Ministry of Education and Science, Republic of Serbia, grant no. 174007.

References

[1] Dajić A. and Koliha J. J., The weighted g-Drazin inverse for operators, J. Aust. Math. Soc. 82 (2007), no. 2, 163–181. 10.1017/S1446788700016013Search in Google Scholar

[2] Drazin M. P., Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514. 10.1080/00029890.1958.11991949Search in Google Scholar

[3] Harte R. E., On quasinilpotents in rings, Panamer. Math. J. 1 (1991), 10–16. Search in Google Scholar

[4] Koliha J. J., A generalized Drazin inverse, Glasg. Math. J. 38 (1996), no. 3, 367–381. 10.1017/S0017089500031803Search in Google Scholar

[5] Koliha J. J., Djordjević D. S. and Cvetković D., Moore–Penrose inverse in rings with involution, Linear Algebra Appl. 426 (2007), no. 2–3, 371–381. 10.1016/j.laa.2007.05.012Search in Google Scholar

[6] Koliha J. J. and Patricio P., Elements of rings with equal spectral idempotents, J. Aust. Math. Soc. 72 (2002), no. 1, 137–152. 10.1017/S1446788700003657Search in Google Scholar

[7] Rakočević V. and Wei Y., A weighted Drazin inverse and applications, Linear Algebra Appl. 350 (2002), 25–39. 10.1016/S0024-3795(02)00297-5Search in Google Scholar

Received: 2014-5-29
Revised: 2014-7-25
Accepted: 2014-8-8
Published Online: 2016-1-7
Published in Print: 2016-12-1

© 2016 by De Gruyter