Generalized derivations with nilpotent values on semiprime rings

Feng Wei

doi:10.1007/s10114-004-0318-2

Generalized derivations with nilpotent values on semiprime rings

Feng Wei^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Let R be a semiprime ring, R_F be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R _F. Furthermore, if there exists a fixed positive integer n such that μ(x)ⁿ = 0 for all x ∈ I, then μ = 0.

Original language	English
Pages (from-to)	453-462
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s10114-004-0318-2
Publication status	Published - Jun 2004

Keywords

Canonical sheaf of semiprime ring
Generalized derivation
Semiprime ring

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10.1007/s10114-004-0318-2

Cite this

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abstract = "Let R be a semiprime ring, RF be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R F. Furthermore, if there exists a fixed positive integer n such that μ(x)n = 0 for all x ∈ I, then μ = 0.",

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AU - Wei, Feng

PY - 2004/6

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N2 - Let R be a semiprime ring, RF be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R F. Furthermore, if there exists a fixed positive integer n such that μ(x)n = 0 for all x ∈ I, then μ = 0.

AB - Let R be a semiprime ring, RF be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of R F. Furthermore, if there exists a fixed positive integer n such that μ(x)n = 0 for all x ∈ I, then μ = 0.

KW - Canonical sheaf of semiprime ring

KW - Generalized derivation

KW - Semiprime ring

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U2 - 10.1007/s10114-004-0318-2

DO - 10.1007/s10114-004-0318-2

M3 - Article

AN - SCOPUS:4744356782

SN - 1439-8516

VL - 20

SP - 453

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 3

ER -

Generalized derivations with nilpotent values on semiprime rings

Abstract

Keywords

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