Taiwanese Journal of Mathematics

ON GENERALIZED DERIVATIONS OF PRIME AND SEMIPRIME RINGS

Shuliang Huang

Full-text: Open access

Abstract

Let $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $n$ a fixed positive integer. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F(x \circ y))^{n} = x \circ y$ for all $x,y \in I$, then $R$ is commutative. We also examine the case where $R$ is a semiprime ring.

Article information

Source
Taiwanese J. Math., Volume 16, Number 2 (2012), 771-776.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406614

Digital Object Identifier
doi:10.11650/twjm/1500406614

Mathematical Reviews number (MathSciNet)
MR2892911

Zentralblatt MATH identifier
1252.16038

Subjects
Primary: 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16U80: Generalizations of commutativity 16W25: Derivations, actions of Lie algebras

Keywords
prime rings semiprime rings generalized derivations GPIs

Citation

Huang, Shuliang. ON GENERALIZED DERIVATIONS OF PRIME AND SEMIPRIME RINGS. Taiwanese J. Math. 16 (2012), no. 2, 771--776. doi:10.11650/twjm/1500406614. https://projecteuclid.org/euclid.twjm/1500406614


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