Derivations of Prime Rings Having Periodic Values

Let R be a prime ring and d ≠ 0 a derivation of R such that d(x)n(x)= d(x), n(x)>1, for all x ∊ R. It is shown that either R is a division ring or R is the ring of all 2 × 2 matrices over a field. Moreover, if the set of integers n(x) is bounded, then R must be the ring of all 2 × 2 matrices over...

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Bibliographic Details
Published in:Chinese journal of mathematics (Taipei, Taiwan) Taiwan), 1986-06, Vol.14 (2), p.95-102
Main Authors: Lin, Jer-Shyong, 林哲雄
Format: Article
Language:English
Subjects:
Algebra
Integers
Logical proofs
Mathematical rings
Mathematical theorems
Matrix identities
Subrings
Online Access:Get full text
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Summary:Let R be a prime ring and d ≠ 0 a derivation of R such that d(x)n(x)= d(x), n(x)>1, for all x ∊ R. It is shown that either R is a division ring or R is the ring of all 2 × 2 matrices over a field. Moreover, if the set of integers n(x) is bounded, then R must be the ring of all 2 × 2 matrices over a finite field.
ISSN:0379-7570