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Skew n-derivations on semiprime rings

Wei Zhang|Yang Liu|Xiaowei Xu
대한수학회 (The Korean Mathematical Society)|2013.11|대한수학회보 (Bulletin of the KMS)|제50권 제6호|pp. 1863-1871

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참고문헌

키워드

prime ringsemiprime ringbiderivationn-derivationskew n- derivation
주제분류수학

초록

For a ring R with an automorphism σ, an n-additive mapping Δ: R × R × · · · × R ! R is called a skew n-derivation with respect to σ if it is always a σ-derivation of R for each argument. Namely, if n − 1 of the arguments are fixed, then Δ is a σ-derivation on the remaining argument. In this short note, from Breˇsar Theorems, we prove that a skew n-derivation (n ≥ 3) on a semiprime ring R must map into the center of R.

Abstract

For a ring R with an automorphism σ, an n-additive mapping Δ: R × R × · · · × R ! R is called a skew n-derivation with respect to σ if it is always a σ-derivation of R for each argument. Namely, if n − 1 of the arguments are fixed, then Δ is a σ-derivation on the remaining argument. In this short note, from Breˇsar Theorems, we prove that a skew n-derivation (n ≥ 3) on a semiprime ring R must map into the center of R.

참고문헌 (30)

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관련 논문AI추천

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