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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[1] 1. Bergen, J., Herstein, I. N. and C. Lanski, Derivations with invertible values, Can. J. Math. 35 (1983), pp. 300–310. Google Scholar

[2] 2. Brauer, R., On a theorem of H. Cartan, Bull. Amer. Math. Soc. 55 (1949), pp. 619–620. Google Scholar

[3] 3. Herstein, I. N., Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1959. Google Scholar

[4] 4. Herstein, I. N., A note on derivations, Can. Math. Bull. 21 (1978), pp. 369–370. Google Scholar

[5] 5. Herstein, I. N., A note on derivations II, Can. Math. Bull. 22 (1979), pp. 509–511. Google Scholar

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