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引用次数: 1
摘要
设$R$是一个素环,$I$是$R$和$f的任意非零理想,而$R$是一个可加映射。然后斜恩格尔条件$langle…langle langle $ $ f (x), x ^ {n_1}捕杀,x ^{甲烷}捕杀,…,x^{n_k} rangle=0$意味着$f (x)=0$ $forall,xin I$提供$2neq$ char $(R)>n_1+n_2+…+n_k, $ where $n_1,n_2,…,n_k$为自然数。这扩展了一些现有的结果。最后,我们还将这一结果推广到ma半环的设置中。
On the additive maps satisfying Skew-Engel conditions
Let $R$ be a prime ring, $I$ be any nonzero ideal of $R$ and $f:Irightarrow R$ be an additivemap. Then skew-Engel condition $langle... langle langle$$f(x),x^{n_1} rangle,x^{n_2} rangle ,...,x^{n_k} rangle=0$ implies that $f (x)=0$ $forall,xin I$ provided $2neq$ char $(R)>n_1+n_2+...+n_k, $ where $n_1,n_2,...,n_k$ are natural numbers. This extends some existing results. In the end, we also generalise this result in the setting of MA-semirings.