Commutativity and Skew-commutativity Conditions with Generalized Derivations
2010 ◽
Vol 17
(spec01)
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pp. 841-850
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Keyword(s):
Let R be a prime ring of characteristic different from 2 with extended centroid C. Let F be a generalized derivation of R, L a non-central Lie ideal of R, f(x1, …, xn) a polynomial over C and f(R)={f(r1, …, rn): ri ∈ R}. We study the following cases: (1) [F(u), F(v)]k=0 for all u, v ∈ L, where k ≥ 1 is a fixed integer; (2) [F(u), F(v)] = 0 for all u, v ∈ f(R); (3) F(u) ◦ F(v)=0 for all u, v ∈ f(R); (4) F(u) ◦ F(v)=u ◦ v for all u, v ∈ f(R). We obtain a description of the structure of R and information on the form of F.
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2018 ◽
Vol 11
(04)
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pp. 1850055
2018 ◽
Vol 17
(03)
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pp. 1850046
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Keyword(s):
2021 ◽
Vol 39
(4)
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pp. 131-141
Keyword(s):
2009 ◽
Vol 80
(2)
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pp. 217-232
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