Derivations with Invertible Values on a Lie Ideal
1988 ◽
Vol 31
(1)
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pp. 103-110
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AbstractLet 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.
2016 ◽
Vol 15
(04)
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pp. 1650058
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2019 ◽
Vol 18
(09)
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pp. 1950167
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Keyword(s):
1988 ◽
Vol 31
(3)
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pp. 280-286
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1972 ◽
Vol 7
(2)
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pp. 191-226
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Keyword(s):
2018 ◽
Vol 17
(03)
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pp. 1850049
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2012 ◽
Vol 49
(4)
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pp. 549-557
2019 ◽
Vol 18
(02)
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pp. 1950031
2009 ◽
Vol 12
(17)
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pp. 5-11