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On the nilpotent commutator of a nilpotent matrix [PDF]

open access: yesLinear and Multilinear Algebra, 2012
We study the structure of the nilpotent commutator $\nb$ of a nilpotent matrix $B$. We show that $\nb$ intersects all nilpotent orbits for conjugation if and only if $B$ is a square--zero matrix. We describe nonempty intersections of $\nb$ with nilpotent orbits in the case the $n \times n$ matrix $B$ has rank $n-2$.
Polona Oblak
exaly   +3 more sources
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Nilpotent polynomials and nilpotent coefficients

Journal of Algebra, 2022
Many mathematicians believe that Köthe conjecture is one of the hardest problem in mathematics. It was started in 1930 and it is still open until now. Some reformulations of the Köthe conjecture were found by many prominent authors. The Köthe conjecture is also equivalent to the condition, for any ring \(R\), the Jacobson radical of \(R[x]\) consists ...
Thomas L. Draper   +2 more
openaire   +2 more sources

Nilpotency of Derivations

Canadian Mathematical Bulletin, 1983
AbstractIt is shown that the nilpotency of a derivation on a 2-torsion free semiprime ring is always an odd number. Examples are provided to show the necessity of the assumptions.
Chung, L. O., Luh, Jiang
openaire   +2 more sources

NILPOTENT LINEAR SEMIGROUPS

International Journal of Algebra and Computation, 2006
We characterize the structure of linear semigroups satisfying certain global and local nilpotence conditions and deduce various Engel-type results. For example, using a form of Zel'manov's solution of the restricted Burnside problem we are able to show that a finitely generated residually finite group is nilpotent if and only if it satisfies a certain
Jespers, Eric, Riley, David
openaire   +2 more sources

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