Traces of permuting n-additive mappings in *-prime rings

Document Type : Research Paper

Authors

Department of Mathematics Aligarh Muslim University, Aligarh, India

Abstract

In this paper, we prove that a nonzero square closed

*

-Lie ideal

U

of a

*

-prime ring

ℜ

of Char

ℜ

\neq

(2^{n} - 2)

is central, if one of the following holds:

(i) δ (x) δ (y) \mp x \circ y \in Z (ℜ),

(i i) [x, y] - δ (x y) δ (y x) \in Z (ℜ),

(i i i) δ (x) \circ δ (y) \mp [x, y] \in Z (ℜ),

(i v) δ (x) \circ δ (y) \mp x y \in Z (ℜ),

(v) δ (x) δ (y) \mp y x \in Z (ℜ),

where

δ

is the trace of

n

-additive map

ϝ : \underset{n - t i m e s}{\underset{⏟}{ℜ \times ℜ \times . . . . \times ℜ}} ⟶ ℜ

for all x, y \in U

Keywords