Annihilators of skew derivations with Engel conditions on prime rings

Taylan Pehlivan; Emine Albas

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 2, page 587-603
  • ISSN: 0011-4642

Abstract

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Let R be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring Q , C the extended centroid of R and a ∈ R . Suppose that δ is a nonzero σ -derivation of R such that a [ δ ( x n ) , x n ] k = 0 for all x ∈ R , where σ is an automorphism of R , n and k are fixed positive integers. Then a = 0 .

How to cite

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Pehlivan, Taylan, and Albas, Emine. "Annihilators of skew derivations with Engel conditions on prime rings." Czechoslovak Mathematical Journal 70.2 (2020): 587-603. <http://eudml.org/doc/297128>.

@article{Pehlivan2020,
abstract = {Let $R$ be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring $Q$, $C$ the extended centroid of $R$ and $a\in R$. Suppose that $\delta $ is a nonzero $\sigma $-derivation of $R$ such that $a[\delta (x^\{n\}),x^\{n\}]_\{k\}=0$ for all $x\in R$, where $\sigma $ is an automorphism of $R$, $n$ and $k$ are fixed positive integers. Then $a=0$.},
author = {Pehlivan, Taylan, Albas, Emine},
journal = {Czechoslovak Mathematical Journal},
keywords = {prime ring; derivation; skew derivation; automorphism},
language = {eng},
number = {2},
pages = {587-603},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Annihilators of skew derivations with Engel conditions on prime rings},
url = {http://eudml.org/doc/297128},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Pehlivan, Taylan
AU - Albas, Emine
TI - Annihilators of skew derivations with Engel conditions on prime rings
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 2
SP - 587
EP - 603
AB - Let $R$ be a noncommutative prime ring of characteristic different from 2, with its two-sided Martindale quotient ring $Q$, $C$ the extended centroid of $R$ and $a\in R$. Suppose that $\delta $ is a nonzero $\sigma $-derivation of $R$ such that $a[\delta (x^{n}),x^{n}]_{k}=0$ for all $x\in R$, where $\sigma $ is an automorphism of $R$, $n$ and $k$ are fixed positive integers. Then $a=0$.
LA - eng
KW - prime ring; derivation; skew derivation; automorphism
UR - http://eudml.org/doc/297128
ER -

References

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