Glasnik Matematicki, Vol. 60, No. 1 (2025), 73-87. \( \)

ON 2MP-, MP2-, AND CMP2-INVERSES IN \(\ast\)-RINGS

Janko Marovt and Dijana Mosić

University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia,, and, IMFM, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia
e-mail:janko.marovt@um.si

Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia
e-mail:dijana@pmf.ni.ac.rs

Abstract.   The notions of a 2MP-inverse, a MP2-inverse, and a C2MP-inverse are extended from the set of all \(m\times n\) complex matrices to the set \(\mathcal{R}^{\dagger}\) of all Moore-Penrose invertible elements in a unital \(\ast \)-ring \(\mathcal{R}\). We study properties of these hybrid generalized inverses and thus generalize some known results. We apply the \((b,c)\)-inverse of \(a\in \mathcal{R}^{\dagger}\) to determine a special case of a 2MP- or MP2-inverse of \(a\) and then use these inverses to solve certain equations which lead to least-squares solutions and the normal equation.

2020 Mathematics Subject Classification.   15A09, 15A10, 17C27

Key words and phrases.   Outer generalized inverse, 2MP-inverse, MP2-inverse, C2MP-inverse, \(\ast\)-ring

https://doi.org/10.3336/gm.60.1.05

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