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Glasnik matematički, Vol. 60 No. 1, 2025.

Original scientific paper

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

On 2MP-, MP2-, and CMP2-inverses in \(\ast\)-rings

Janko Marovt orcid id orcid.org/0000-0001-5325-4061 ; University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia,, and, IMFM, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia
Dijana Mosić orcid id orcid.org/0000-0002-3255-9322 ; Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia

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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.

Keywords

Outer generalized inverse, 2MP-inverse, MP2-inverse, C2MP-inverse, \(\ast\)-ring

Hrčak ID:

332478

URI

https://hrcak.srce.hr/332478

Publication date:

15.8.2026.

Visits: 488 *

Publication date: 10 June 2025

Volume: Vol 60

Issue: Svezak 1

Pages: 73-87

DOI: 10.3336/gm.60.1.05

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Outer generalized inverse, 2MP-inverse, MP2-inverse, C2MP-inverse, \(\ast\)-ring

On 2MP-, MP2-, and CMP2-inverses in \(\ast\)-rings

Janko Marovt[1]

Email: janko.marovt@um.si

Dijana Mosić[2]

Email: dijana@pmf.ni.ac.rs

 

[1] University of Maribor, Faculty of Economics and Business, Razlagova 14, SI-2000 Maribor, Slovenia,, and, IMFM, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia

[2] Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia

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.

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