A Jordan canonical form for nilpotent elements in an arbitrary ring

A Jordan canonical form for nilpotent elements in an arbitrary ring

In this paper we give an inductive new proof of the Jordan canonical form of a nilpotent element in an arbitrary ring. If a∈R is a nilpotent element of index n with von Neumann regular an−1, we decompose a=ea+(1−e)a with ea∈eRe≅Mn(S) a Jordan block of size n over a corner S of R, and (1−e)a nilpoten...

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Veröffentlicht in:Linear algebra and its applications 2019-11, Vol.581, p.324-335
Hauptverfasser: García, Esther, Gómez Lozano, Miguel, Muñoz Alcázar, Rubén, Vera de Salas, Guillermo
Format: Artikel
Sprache:eng
Schlagworte:
Canonical forms
Jordan canonical form
Linear algebra
nilpotent
Rings (mathematics)
von Neumann regular
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Zusammenfassung:In this paper we give an inductive new proof of the Jordan canonical form of a nilpotent element in an arbitrary ring. If a∈R is a nilpotent element of index n with von Neumann regular an−1, we decompose a=ea+(1−e)a with ea∈eRe≅Mn(S) a Jordan block of size n over a corner S of R, and (1−e)a nilpotent of index
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.07.016