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An identity on automorphisms of Lie ideals in prime rings

An identity on automorphisms of Lie ideals in prime rings In the present paper it is shown that a prime ring R with center Z satisfies $$s_4$$ s 4 , the standard identity in four variables if R admits a non-identity automorphism $$\sigma $$ σ such that $$[u^\sigma ,u]^nu^\sigma \in Z$$ [ u σ , u ] n u σ ∈ Z for all u in some non-central Lie ideal L of R, whenever $$char(R)>n$$ c h a r ( R ) > n or $$char(R)=0$$ c h a r ( R ) = 0 , where n is a fixed positive integer. This result is in the spirit of theorems such as Posner’s second theorem or the Herstein’s theorem on derivations with central values. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL'UNIVERSITA' DI FERRARA Springer Journals

An identity on automorphisms of Lie ideals in prime rings

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Università degli Studi di Ferrara
Subject
Mathematics; Mathematics, general; Analysis; Geometry; History of Mathematical Sciences; Numerical Analysis; Algebraic Geometry
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-016-0240-4
Publisher site
See Article on Publisher Site

Abstract

In the present paper it is shown that a prime ring R with center Z satisfies $$s_4$$ s 4 , the standard identity in four variables if R admits a non-identity automorphism $$\sigma $$ σ such that $$[u^\sigma ,u]^nu^\sigma \in Z$$ [ u σ , u ] n u σ ∈ Z for all u in some non-central Lie ideal L of R, whenever $$char(R)>n$$ c h a r ( R ) > n or $$char(R)=0$$ c h a r ( R ) = 0 , where n is a fixed positive integer. This result is in the spirit of theorems such as Posner’s second theorem or the Herstein’s theorem on derivations with central values.

Journal

ANNALI DELL'UNIVERSITA' DI FERRARASpringer Journals

Published: Mar 9, 2016

References