半素环上加性映射的恒等式

Q3 Mathematics
A. Z. Ansari, N. Rehman
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引用次数: 0

摘要

考虑一个环$R$,它是半素数并且具有$k$ -扭自由度。如果$F, d : R\to R$是两个相加的映射,满足$R.$中的每个$x$的代数恒等式$$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$,那么$F$将是一个广义的派生,在$R$上有一个关联的派生$d$。另一方面,本文还推导出$f$是一个广义左导,在$R$上有一个链接左导$\delta$,如果它们满足$R$和$k\in \{2, m, n, (n+m-1)!\}$中每个$x$的代数恒等式$$f(x^{n+m})=x^n f(x^m)+ x^m \delta(x^n)$$,最后给出了在Banach代数上的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Identities on additive mappings in semiprime rings
Consider a ring $R$, which is semiprime and also having $k$-torsion freeness. If $F, d : R\to R$ are two additive maps fulfilling the algebraic identity $$F(x^{n+m})=F(x^m) x^n+ x^m d(x^n)$$ for each $x$ in $R.$ Then $F$ will be a generalized derivation having $d$ as an associated derivation on $R$. On the other hand, in this article, it is also derived that $f$ is a generalized left derivation having a linked left derivation $\delta$ on $R$ if they satisfy the algebraic identity $$f(x^{n+m})=x^n f(x^m)+ x^m \delta(x^n)$$ for each $x$ in $R$ and $k\in \{2, m, n, (n+m-1)!\}$ and at last an application on Banach algebra is presented.
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来源期刊
Matematychni Studii
Matematychni Studii Mathematics-Mathematics (all)
CiteScore
1.00
自引率
0.00%
发文量
38
期刊介绍: Journal is devoted to research in all fields of mathematics.
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