Let R be a prime ring, Z(R) its center, C its extended centroid, L a Lie ideal of R, F a generalized skew derivation associated with a skew derivation d and automorphism α. Assume that there exist t≥ 1 and m, n≥ 0 fixed integers such that vu= umF(uv) tun for all u, v∈ L. Then it is shown that either L is central or char (R) = 2 , R⊆ M2(C) , the ring of 2 × 2 matrices over C, L is commutative and u2∈ Z(R) , for all u∈ L. In particular, if L= [ R, R] , then R is commutative. © 2018, Indian Academy of Sciences.
A note on generalized skew derivations on Lie ideals
De Filippis V.
2018-01-01
Abstract
Let R be a prime ring, Z(R) its center, C its extended centroid, L a Lie ideal of R, F a generalized skew derivation associated with a skew derivation d and automorphism α. Assume that there exist t≥ 1 and m, n≥ 0 fixed integers such that vu= umF(uv) tun for all u, v∈ L. Then it is shown that either L is central or char (R) = 2 , R⊆ M2(C) , the ring of 2 × 2 matrices over C, L is commutative and u2∈ Z(R) , for all u∈ L. In particular, if L= [ R, R] , then R is commutative. © 2018, Indian Academy of Sciences.File in questo prodotto:
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