On a pair of (α, β)-derivations of semiprime rings

Muhammad Anwar Chaudhry; Allah Bakhsh Thaheem

doi:10.1007/s00010-004-2763-5

On a pair of (α, β)-derivations of semiprime rings

Muhammad Anwar Chaudhry^*
, Allah Bakhsh Thaheem

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

4 Scopus citations

Abstract

Among other results we show that if α, β are centralizing epimorphisms and f, g are (α, β)-derivations of a 2-torsion free semiprime ring R such that f(x)x + xg(x) = 0 for all x R, then f(u)[x, y] = g(u)[x, y] = 0 for all x, y, u ∈ R; in particular, f and g map R into its center.

Original language	English
Pages (from-to)	224-230
Number of pages	7
Journal	Aequationes Mathematicae
Volume	69
Issue number	3
DOIs	https://doi.org/10.1007/s00010-004-2763-5
State	Published - May 2005

Keywords

(α, β)-derivation
Centralizing map
Commuting map
Epimorphism
Prime ring
Semiprime ring
α-derivation

ASJC Scopus subject areas

General Mathematics
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s00010-004-2763-5

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title = "On a pair of (α, β)-derivations of semiprime rings",

abstract = "Among other results we show that if α, β are centralizing epimorphisms and f, g are (α, β)-derivations of a 2-torsion free semiprime ring R such that f(x)x + xg(x) = 0 for all x R, then f(u)[x, y] = g(u)[x, y] = 0 for all x, y, u ∈ R; in particular, f and g map R into its center.",

keywords = "(α, β)-derivation, Centralizing map, Commuting map, Epimorphism, Prime ring, Semiprime ring, α-derivation",

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T1 - On a pair of (α, β)-derivations of semiprime rings

AU - Chaudhry, Muhammad Anwar

AU - Thaheem, Allah Bakhsh

PY - 2005/5

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N2 - Among other results we show that if α, β are centralizing epimorphisms and f, g are (α, β)-derivations of a 2-torsion free semiprime ring R such that f(x)x + xg(x) = 0 for all x R, then f(u)[x, y] = g(u)[x, y] = 0 for all x, y, u ∈ R; in particular, f and g map R into its center.

AB - Among other results we show that if α, β are centralizing epimorphisms and f, g are (α, β)-derivations of a 2-torsion free semiprime ring R such that f(x)x + xg(x) = 0 for all x R, then f(u)[x, y] = g(u)[x, y] = 0 for all x, y, u ∈ R; in particular, f and g map R into its center.

KW - (α, β)-derivation

KW - Centralizing map

KW - Commuting map

KW - Epimorphism

KW - Prime ring

KW - Semiprime ring

KW - α-derivation

UR - https://www.scopus.com/pages/publications/21244491634

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DO - 10.1007/s00010-004-2763-5

M3 - Article

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SN - 0001-9054

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SP - 224

EP - 230

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 3

ER -

On a pair of (α, β)-derivations of semiprime rings

Abstract

Keywords

ASJC Scopus subject areas

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