A locally nilpotent radical in some classes of right-alternative rings

1976 ◽  
Vol 17 (2) ◽  
pp. 265-280 ◽  
Author(s):  
S. V. Pchelintsev
Keyword(s):  
Nilpotent Radical ◽  
Locally Nilpotent

A locally nilpotent radical of nonassociative rings

1971 ◽  
Vol 10 (4) ◽  
pp. 219-224 ◽  
Author(s):  
G. V. Dorofeev
Keyword(s):  
Nilpotent Radical ◽  
Locally Nilpotent

scholarly journals On a locally nilpotent radical Jacobson for special Lie algebras

2021 ◽  
Vol 22 (1) ◽  
pp. 234-272
Author(s):  
Olga Alexandrovna Pikhtilkova ◽  
Elena Vladimirovna Mescherina ◽  
Anna Nikolaevna Blagovisnava ◽  
Elena Vladislavovna Pronina ◽  
Olga Alekseevna Evseeva
Keyword(s):  
Lie Algebras ◽  
Nilpotent Radical ◽  
Locally Nilpotent

Classical Radicals of Invariants of Algebraic Skew Derivations

2022 ◽  
Vol 29 (01) ◽  
pp. 53-66
Author(s):  
Jeffrey Bergen ◽  
Piotr Grzeszczuk
Keyword(s):  
Hopf Algebra ◽  
Lie Algebra ◽  
Jacobson Radical ◽  
Prime Radical ◽  
Nilpotent Radical ◽  
Enveloping Algebra ◽  
Locally Nilpotent ◽  
Nil Radical

Let [Formula: see text] be an automorphism and[Formula: see text] be a [Formula: see text]-skew [Formula: see text]-derivation of an [Formula: see text]-algebra [Formula: see text]. We prove that if [Formula: see text] is semiprimitive and [Formula: see text] is algebraic, then the subalgebra [Formula: see text] has nilpotent Jacobson radical. Using this result, we obtain similar relations for the Baer prime radical, the Levitzki locally nilpotent radical, and the Köthe nil radical when the field [Formula: see text] is uncountable. Then we apply it to actions of the [Formula: see text]-dimensional Taft Hopf algebra [Formula: see text] and the [Formula: see text]-analogue [Formula: see text] of the enveloping algebra of the Lie algebra [Formula: see text].

Locally nilpotent ideals of a Lie algebra

1967 ◽  
Vol 63 (2) ◽  
pp. 257-272 ◽  
Author(s):  
B. Hartley
Keyword(s):  
Lie Algebra ◽  
Characteristic Zero ◽  
Nilpotent Radical ◽  
Finite Dimensional ◽  
Locally Nilpotent

The purpose of this paper is to investigate the locally nilpotent radical of a Lie algebra L over a field of characteristic zero, its behaviour under derivations of L, and its behaviour with regard to finite-dimensional nilpotent subinvariant and ascendant subalgebras of L.

scholarly journals Left 3-Engel elements in groups of exponent 60

2018 ◽  
Vol 28 (04) ◽  
pp. 673-695 ◽  
Author(s):  
Gareth Tracey ◽  
Gunnar Traustason
Keyword(s):  
Nilpotent Radical ◽  
Engel Elements ◽  
Locally Nilpotent ◽  
Engel Element

Let [Formula: see text] be a group and let [Formula: see text] be a left [Formula: see text]-Engel element of order dividing [Formula: see text]. Suppose furthermore that [Formula: see text] has no elements of order [Formula: see text], [Formula: see text] and [Formula: see text]. We show that [Formula: see text] is then contained in the locally nilpotent radical of [Formula: see text]. In particular, all the left [Formula: see text]-Engel elements of a group of exponent [Formula: see text] are contained in the locally nilpotent radical.

scholarly journals On the influence of ideals and self-idealizing subalgebras on the structure of Leibniz algebras

2021 ◽  
pp. 12-17
Author(s):  
L.A. Kurdachenko ◽  
A.A. Pypka ◽  
I.Ya. Subbotin
Keyword(s):  
Leibniz Algebra ◽  
Nilpotent Radical ◽  
Leibniz Algebras ◽  
Locally Nilpotent ◽  
Dimension 2

The subalgebra A of a Leibniz algebra L is self-idealizing in L, if A = IL (A) . In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing. More precisely, we obtain a description of such Leibniz algebras for the cases where the locally nilpotent radical is Abelian non-cyclic, non-Abelian noncyclic, and cyclic of dimension 2.

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