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Posner's second theorem and annihilator conditions with generalized skew derivations

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De Filippis V., Wei F.

Colloquium Mathematicum

2012

tom 129

nr 1

61-74

Let 𝓡 be a prime ring of characteristic different from 2, $𝒬_r$ be its right Martindale quotient ring and 𝓒 be its extended centroid. Suppose that 𝒢 is a non-zero generalized skew derivation of 𝓡 and f(x₁,..., xₙ) is a non-central multilinear polynomial over 𝓒 with n non-commuting variables. If there exists a non-zero element a of 𝓡 such that a[𝒢 (f(r₁,..., rₙ)),f(r₁, ..., rₙ)] = 0 for all r₁, ..., rₙ ∈ 𝓡, then one of the following holds: (a) there exists λ ∈ 𝓒 such that 𝒢 (x) = λx for all x ∈ 𝓡; (b) there exist $q ∈ 𝒬_r$ and λ ∈ 𝓒 such that 𝒢 (x) = (q+λ)x + xq for all x ∈ 𝓡 and f(x₁, ..., xₙ)² is central-valued on 𝓡.

Ograniczanie wyników

1 Colloquium Mathematicum

1 De Filippis V.

1 Wei F.

1 2012

Wyniki wyszukiwania

Posner's second theorem and annihilator conditions with generalized skew derivations