Generalized Core-nilpotent Decomposition of Ring Elements

Savitha Varkady (), Umashankara Kelathaya () and Manjunatha Prasad Karantha ()
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Savitha Varkady: Prasanna School of Public Health
Umashankara Kelathaya: Prasanna School of Public Health
Manjunatha Prasad Karantha: Prasanna School of Public Health

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1102-1109

Abstract: Abstract Different kinds of decompositions of a square matrix have been studied in the literature by altering the conditions on the summands of core-nilpotent decomposition. Motivated by the observation that for an element from an associative ring the Drazin inverse and the core-nilpotent decomposition coexist, and many of among the techniques which are useful in the case of matrices fail in the case dealing with the elements from an associative ring, the theory of generalized inverse and the minus partial order are used to characterize and study the generalized core-nilpotent decomposition of an element from an associative ring.

Keywords: Core-nilpotent decomposition; Generalized inverses; Minus partial order; 15A09; 06A06 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00825-2

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