On G-Drazin partial order in rings

Dolinar, Gregor (author), Kuzma, Bojan (author), Marovt, Janko (author), Mosić, Dijana (author)

We extend the concept of a G-Drazin inverse from the set $M_n$ of all $n × n$ complex matrices to the set $\mathcal{R}^\mathcal{D}$ of all Drazin invertible elements in a ring $\mathcal{R}$ with identity. We also generalize a partial order induced by G-Drazin inverses from $M_n$ to the set of all regular elements in $\mathcal{R}^\mathcal{D}$, study its properties, compare it to known partial orders, and generalize some known results.

• Language: English
• Keywords: Drazin inverse, core-nilpotent decomposition, partial order, annihilator, ring
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: Str. 176-192
• Numbering: Vol. 173, iss. 1
• PID: 20.500.12556/RUL-160337
• UDC: 512
• ISSN on article: 0236-5294
• DOI: 10.1007/s10474-024-01429-8
• COBISS.SI-ID: 205138179
• Publication date in RUL: 26.08.2024

Record is a part of a journal

• Title: Acta mathematica Hungarica
• Shortened title: Acta math. Hung.
• Publisher: Akadémiai Kiadó, Springer
• ISSN: 0236-5294
• COBISS.SI-ID: 27704576

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.