Results 221 to 230 of about 27,601 (255)

Semilocal rings with Engel conditions

Archiv der Mathematik, 2006
The relation between the Engel structure of a semilocal ring and that of its multiplicative group is investigated. Suppose that every local ring whose multiplicative group satisfies an m-Engel condition for some positive integer m is an f (m)-Engel ring for some function f .
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An Engel condition with generalized derivations on multilinear polynomials

Israel Journal of Mathematics, 2007
Let \(R\) be a prime ring with center \(Z(R)\), extended centroid \(C\), nonzero right ideal \(I\), right Utumi quotient ring \(U\), and nonzero generalized derivation \(g\). Set \(f=f(x_1,\dots,x_n)\), a multilinear polynomial over \(C\) in noncommuting indeterminates so that the evaluations in \(R\) satisfy \(f(R^n)\nsubseteq C\). The purpose of this
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On the additive maps satisfying skew-Engel conditions

2017
Summary: Let \(R\) be a prime ring, \(I\) be any nonzero ideal of \(R\) and \(f:I\to R\) be an additive map. Then skew-Engel condition \(\langle\ldots\langle\langle f(x),x^{n_1}\rangle,x^{n_2}\rangle,\ldots, x^{n_k}\rangle=0\) implies that \(f(x)=0\;\forall x\in I\) provided \(2\neq \operatorname{char}(R) > n_1 + n_2 + \ldots + n_k\), where \(n_1,n_2 ...
Nadeem, M., Aslam, M., Ahmed, Y.
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Annihilators of skew derivations with Engel conditions on prime rings

Czechoslovak Mathematical Journal, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pehlivan, Taylan, Albas, Emine
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Annihilators of derivations with Engel conditions on lie ideals

Rendiconti del Circolo Matematico di Palermo, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A condition for an area-preserving mapping to be in the Engel’s form

Journal of Mathematical Physics, 2000
We establish explicit expressions of restrictions on the coefficients of nonlinear terms in a two-dimensional area-preserving polynomial map imposed by the property of area preserving. We also establish a necessary and sufficient condition for a two-dimensional area-preserving generic polynomial map to be in the Engel’s form.
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Engel donditions on groups

1964
Let g,c denote positive integers. A group is said to have type (g→c) if every subgroup which can be generated by g elements is nilpotent of class at most c. A result of R. H. Bruck shows that groups of type (4→5) without elements of order 2 are nilpotent of class at most 7.
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A Generalization of Engel Conditions with Derivations in Rings

Communications in Algebra, 2011
Let R be a prime ring of characteristic different from 2 with Z the center of R and d a nonzero derivation of R. Let k, m, n be fixed positive integers. If ([d(x k ), x k ] n ) m  ∈ Z for all x ∈ R, then R satisfies S 4, the standard identity in 4 variables.
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The nilpotency of Leibniz algebras with Engel condition

Moscow University Mathematics Bulletin, 2011
It is proved that a Leibniz algebra over a field of zero characteristic with the Engel condition is nilpotent.
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Engel Elements in Groups with the Minimal Condition

Journal of the London Mathematical Society, 1973
Martin, J. E., Pamphilon, J. A.
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