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Generalized skew-derivations annihilating and centralizing on multilinear polynomials in prime rings
PRIYADWIP DAS BASUDEB DHARA SUKHENDU KAR
Research Article Volume 129 Issue 2 April 2019 Article ID 0018
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https://www.ias.ac.in/article/fulltext/pmsc/129/02/0018 -
Keywords
Prime ring ;derivation ;generalized derivation ;generalized skew derivation ;extended centroid -
Abstract
Let $R$ be a prime ring of characteristic $\neq 2$, $Qr$ its right Martindale quotient ring, $C$ its extended centroid, $F \neq 0$ a generalized skew derivation of $R, f (x_{1}, . . . , x_{n})$ a multilinear polynomial over $C$ not central-valued on $R$ and $S$ the set of all evaluations of $f (x_{1}, . . . , x_{n})$ in $R$. If $a[F(x), x] \in C$ for all $x \in S$, then there exist $\lambda \in C$ and $b \in Qr$ such that $F(x) = bx + xb + \lambda x$, for all $x \in R$ and one of the following holds:(1) $b \in C$;(2) $f (x_{1}, . . . , x_{n})^{2}$ is central-valued on $R$;(3) $R$ satisfies $s_{4}$, the standered identity of degree 4.
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Author Affiliations
PRIYADWIP DAS1 BASUDEB DHARA2 SUKHENDU KAR1
- Department of Mathematics, Jadavpur University, Kolkata 700 032, India
- Department ofMathematics, Belda College, Belda, Paschim Medinipur 721 424, India
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Dates
- Published
- 1 April 2019
- Manuscript received
- 19 October 2017
- Manuscript revised
- 24 November 2017
- Accepted
- 30 November 2017
- Early published
- Unedited version published online
- Final version published online
- 14 February 2019
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Proceedings – Mathematical Sciences
Volume 133, 2023
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