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Automorphism Groups of Deformations and Quantizations of Kleinian Singularities. [PDF]

Transform Groups
Castellan S.
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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, Pace P. Nielsen, Janez Šter   +2 more
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Core-Nilpotent decomposition and new generalized inverses of finite potent endomorphisms

Linear and multilinear algebra, 2020
The aim of this work is to prove the existence and uniqueness of a core-nilpotent decomposition of finite potent endomorphisms on arbitrary vector spaces. This decomposition generalized the well-known core-nilpotent decomposition of complex -matrices. As
F. Romo
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When nilpotent elements generate nilpotent ideals

Journal of Algebra and Its Applications, 2023
We study the natural class of rings where each nilpotent element generates a nilpotent ideal, calling them the strongly 2-primal rings. We derive many basic properties of these rings, analyze their behavior under standard ring constructions and extensions, and taxonomize their relationship to other natural generalizations of commutativity.
Nielsen, Pace P., Szabo, Steve
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Nilpotent Structures in Ergodic Theory

Mathematical Surveys and Monographs, 2018
Nilpotent Structures in Ergodic Theory Bernard Host, Université Paris-Est Marne-la-Vallée, Champssur-Marne, France, and Bryna Kra, Northwestern University, Evanston, IL Nilsystems play a key role in the structure theory of measure preserving systems ...
B. Host, Bryna Kra
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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
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The Algebraic and Geometric Classification of Nilpotent Bicommutative Algebras

Algebras and Representation Theory, 2019
We classify the complex 4-dimensional nilpotent bicommutative algebras from both algebraic and geometric approaches.
I. Kaygorodov, Pilar Páez-Guillán, Vasily Voronin   +2 more
semanticscholar   +1 more source

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
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Minimal Non-nilpotent and Locally Nilpotent Fusion Systems

Algebra Colloquium, 2016
The main purpose of this note is to show that there is a one-to-one correspondence between minimal non-nilpotent (resp., locally nilpotent) saturated fusion systems and finite p′-core-free p-constrained minimal non-nilpotent (resp., locally p-nilpotent) groups.
Liao, Jun, Liu, Yanjun
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NILPOTENCY IN UNCOUNTABLE GROUPS

Journal of the Australian Mathematical Society, 2016
The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}
De Giovanni, Francesco, Trombetti, Marco
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