Inverse complements and strongly unit regular elements

Umashankara Kelathaya, Savitha Varkady, Manjunatha Prasad Karantha

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, the notion of "strongly unit regular element", for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.

Original languageEnglish
Article number2250190
JournalJournal of Algebra and Its Applications
DOIs
Publication statusAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Applied Mathematics

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