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

Q4 Mathematics Journal of Algebra and Related Topics Pub Date : 2020-12-01 DOI:10.22124/JART.2020.16288.1200

A. Ali, K. Kumar

引用次数: 0

Abstract

In this paper, we prove that a nonzero square closed $*$-Lie ideal $U$ of a $*$-prime ring $Re$ of Char $Re$ $neq$ $(2^{n}-2)$ is central, if one of the following holds: $(i)delta(x)delta(y)mp xcirc yin Z(Re),$ $(ii)[x,y]-delta(xy)delta(yx)in Z(Re),$ $(iii)delta(x)circ delta(y)mp [x,y]in Z(Re),$ $(iv)delta(x)circ delta(y)mp xyin Z(Re),$ $(v) delta(x)delta(y)mp yxin Z(Re),$ where $delta$ is the trace of $n$-additive map $digamma: underbrace{Retimes Retimes....times Re}_{n-times}longrightarrow Re$,$~mbox{for all}~ x,yin U$.

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*素环中置换n-加性映射的迹

在本文中，我们证明了$ $*$-素环$ $Re$ $ $neq$ $ $ $(2^{n}-2)$ $的非零平方闭合$ $ $ $ $是中心理想$U$，如果满足下列条件之一:$ $(i)delta(x)delta(y)mp xcirc yin Z(Re)，$ $(ii)[x,y]-delta(xy)delta(yx) In Z(Re)，$ $(iii)delta(x)circ delta(y)mp [x,y] In Z(Re)，$ $(iv)delta(x)circ delta(y)mp [x,y] In Z(Re)，$ $(v) delta(x)delta(y)mp yxin Z(Re)，$ $其中$delta$是$n的轨迹$ $-可加映射$digamma:下划线{Retimes Retimes....* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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