Derivations with Engel conditions in prime and semiprime rings

Shuliang Huang

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 1135-1140
  • ISSN: 0011-4642

Abstract

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Let R be a prime ring, I a nonzero ideal of R , d a derivation of R and m , n fixed positive integers. (i) If ( d [ x , y ] ) m = [ x , y ] n for all x , y ∈ I , then R is commutative. (ii) If Char R ≠ 2 and [ d ( x ) , d ( y ) ] m = [ x , y ] n for all x , y ∈ I , then R is commutative. Moreover, we also examine the case when R is a semiprime ring.

How to cite

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Huang, Shuliang. "Derivations with Engel conditions in prime and semiprime rings." Czechoslovak Mathematical Journal 61.4 (2011): 1135-1140. <http://eudml.org/doc/196816>.

@article{Huang2011,
abstract = {Let $R$ be a prime ring, $I$ a nonzero ideal of $R$, $d$ a derivation of $R$ and $m, n$ fixed positive integers. (i) If $(d[x,y])^\{m\}=[x,y]_\{n\}$ for all $x,y\in I$, then $R$ is commutative. (ii) If $\mathop \{\rm Char\}R\ne 2$ and $[d(x),d(y)]_\{m\}=[x,y]^\{n\}$ for all $x,y\in I$, then $R$ is commutative. Moreover, we also examine the case when $R$ is a semiprime ring.},
author = {Huang, Shuliang},
journal = {Czechoslovak Mathematical Journal},
keywords = {prime and semiprime rings; ideal; derivation; GPIs; prime rings; semiprime rings; derivations; GPIs; Engel conditions; commutativity theorems},
language = {eng},
number = {4},
pages = {1135-1140},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derivations with Engel conditions in prime and semiprime rings},
url = {http://eudml.org/doc/196816},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Huang, Shuliang
TI - Derivations with Engel conditions in prime and semiprime rings
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 1135
EP - 1140
AB - Let $R$ be a prime ring, $I$ a nonzero ideal of $R$, $d$ a derivation of $R$ and $m, n$ fixed positive integers. (i) If $(d[x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. (ii) If $\mathop {\rm Char}R\ne 2$ and $[d(x),d(y)]_{m}=[x,y]^{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover, we also examine the case when $R$ is a semiprime ring.
LA - eng
KW - prime and semiprime rings; ideal; derivation; GPIs; prime rings; semiprime rings; derivations; GPIs; Engel conditions; commutativity theorems
UR - http://eudml.org/doc/196816
ER -

References

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