On Derivations in Prime Rings and a Question of Herstein
Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 339-344
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In [2], Herstein proves the following result:Theorem. Let R be a prime ring, d≠0 a derivation of R such that d(x) d(y) = d(y) d(x) for all x, y ∈ R. Then, if char r≠2, R is commutative, and if char R = 2, R is commutative or an order in a simple algebra which is 4-dimensional over its center.
Kovacs, Amos. On Derivations in Prime Rings and a Question of Herstein. Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 339-344. doi: 10.4153/CMB-1979-042-0
@article{10_4153_CMB_1979_042_0,
author = {Kovacs, Amos},
title = {On {Derivations} in {Prime} {Rings} and a {Question} of {Herstein}},
journal = {Canadian mathematical bulletin},
pages = {339--344},
year = {1979},
volume = {22},
number = {3},
doi = {10.4153/CMB-1979-042-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-042-0/}
}
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