DERIVATIONS WITH ANNIHILATOR CONDITIONS IN PRIME RINGS

Title & Authors
DERIVATIONS WITH ANNIHILATOR CONDITIONS IN PRIME RINGS
Dhara, Basudeb; Kar, Sukhendu; Mondal, Sachhidananda;

Abstract
Let R be a prime ring, I a nonzero ideal of R, $\small{d}$ a derivation of R, $\small{m({\geq}1)}$, $\small{n({\geq}1)}$ two fixed integers and $\small{a{\in}R}$. (i) If $\small{a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx))^m=0}$ for all $\small{x,y{\in}I}$, then either $\small{a=0}$ or R is commutative; (ii) If $\small{char(R){\neq}2}$ and $\small{a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx)){\in}Z(R)}$ for all $\small{x,y{\in}I}$, then either $\small{a=0}$ or R is commutative.
Keywords
prime ring;derivation;extended centroid;
Language
English
Cited by
1.
A note on annihilator conditions in prime rings, Rendiconti del Circolo Matematico di Palermo (1952 -), 2017
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