Geodesic
Derivations with Invertible Values on a Lie Ideal
Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 103-110

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Let R be a ring which possesses a unit element, a Lie ideal U ⊄ Z, and a derivation d such that d(U) ≠ 0 and d(u) is 0 or invertible, for all u∈ U. We prove that R must be either a division ring D or D2, the 2 X 2 matrices over a division ring unless d is not inner, R is not semiprime, and either 2R or 3R is 0. We also examine for which division rings D, D2 can possess such a derivation and study when this derivation must be inner.
DOI : 10.4153/CMB-1988-016-x
Mots-clés : 16A68, 16A72 
Bergen, Jeffrey; Carini, L. Derivations with Invertible Values on a Lie Ideal. Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 103-110. doi: 10.4153/CMB-1988-016-x
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     author = {Bergen, Jeffrey and Carini, L.},
     title = {Derivations with {Invertible} {Values} on a {Lie} {Ideal}},
     journal = {Canadian mathematical bulletin},
     pages = {103--110},
     year = {1988},
     volume = {31},
     number = {1},
     doi = {10.4153/CMB-1988-016-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-016-x/}
}
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