Inverse complements and strongly unit regular elements

Umashankara Kelathaya; Savitha Varkady; Manjunatha Prasad Karantha

doi:10.1142/S0219498822501900

Inverse complements and strongly unit regular elements

Umashankara Kelathaya, Savitha Varkady, Manjunatha Prasad Karantha

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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 language	English
Article number	2250190
Journal	Journal of Algebra and Its Applications
Volume	21
Issue number	10
DOIs	https://doi.org/10.1142/S0219498822501900
Publication status	Published - 01-10-2022

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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N2 - 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.

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Inverse complements and strongly unit regular elements

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