Results 211 to 220 of about 71,809 (229)

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
openaire   +2 more sources

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
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

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

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
openaire   +2 more sources

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
openaire   +2 more sources

Nilpotence, projectivity, decomposability

Siberian Mathematical Journal, 1992
A concept of (quasi) commutator is introduced. (The notion is somewhat different from the concept of commutator given by R. Freese and R. McKenzie.) Next it is shown that the consideration of projective algebras can be restricted to the consideration of projective algebras in maximal abelian subvarieties.
openaire   +3 more sources

RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT

International Journal of Algebra and Computation, 2011
Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, observing the structure of nilpotent elements in Armendariz rings and introducing the notion of nil-Armendariz rings. The class of nil-Armendariz rings contains Armendariz rings and NI rings.
Kwak, Tai Keun, Lee, Yang
openaire   +2 more sources

NILPOTENT QUANTUM MECHANICS

International Journal of Modern Physics A, 2010
We develop a generalized quantum mechanical formalism based on the nilpotent commuting variables (η-variables). In the nonrelativistic case such formalism provides natural realization of a two-level system (qubit). Using the space of η-wavefunctions, η-Hilbert space and generalized Schrödinger equation we study properties of pure multiqubit systems and
openaire   +2 more sources

Characteristically Nilpotent Algebras

Canadian Journal of Mathematics, 1971
Our aim in this paper is to extend (Theorem 1.7) to general algebras a classical result of Lie algebras due to Léger and Togo [6]. This extension requires, in turn, extension to general algebras of the concept of characteristically nilpotent algebras introduced by Dixmier and Lister [3] for Lie algebras. Based on this extended concept, we introduce in §
openaire   +1 more source