Derivations with power central values on Lie ideals in prime rings

Basudeb Dhara; Rajendra K. Sharma

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 1, page 147-153
  • ISSN: 0011-4642

Abstract

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Let R be a prime ring of char R ≠ 2 with a nonzero derivation d and let U be its noncentral Lie ideal. If for some fixed integers n 1 ≥ 0 , n 2 ≥ 0 , n 3 ≥ 0 , ( u n 1 [ d ( u ) , u ] u n 2 ) n 3 ∈ Z ( R ) for all u ∈ U , then R satisfies S 4 , the standard identity in four variables.

How to cite

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Dhara, Basudeb, and Sharma, Rajendra K.. "Derivations with power central values on Lie ideals in prime rings." Czechoslovak Mathematical Journal 58.1 (2008): 147-153. <http://eudml.org/doc/31204>.

@article{Dhara2008,
abstract = {Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^\{n_1\}[d(u),u]u^\{n_2\})^\{n_3\}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.},
author = {Dhara, Basudeb, Sharma, Rajendra K.},
journal = {Czechoslovak Mathematical Journal},
keywords = {prime ring; derivation; extended centroid; martindale quotient ring; prime rings; derivations; extended centroids; Martindale quotient rings; additive mappings; noncentral Lie ideals},
language = {eng},
number = {1},
pages = {147-153},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derivations with power central values on Lie ideals in prime rings},
url = {http://eudml.org/doc/31204},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Dhara, Basudeb
AU - Sharma, Rajendra K.
TI - Derivations with power central values on Lie ideals in prime rings
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 147
EP - 153
AB - Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.
LA - eng
KW - prime ring; derivation; extended centroid; martindale quotient ring; prime rings; derivations; extended centroids; Martindale quotient rings; additive mappings; noncentral Lie ideals
UR - http://eudml.org/doc/31204
ER -

References

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