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Derivations of prime and semiprime rings

Hulya G. Inceboz|Nurcan Argac
대한수학회 (The Korean Mathematical Society)|2009.09|대한수학회지 (Journal of the KMS)|제46권 제5호|pp. 997-1005

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참고문헌

키워드

derivationsprime and semiprime ringsleft Utumi quotient ringsdifferential identities
주제분류수학

초록

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x))^{n}=xy+yx for all x,y∈ I, then R is commutative. (ii) If charR≠2 and (d(x)y+xd(y)+d(y)x+yd(x))^{n}-(xy+yx) is central for all x,y ∈ I, then R is commutative. We also examine the case where R is a semiprime ring.

Abstract

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+yd(x))^{n}=xy+yx for all x,y∈ I, then R is commutative. (ii) If charR≠2 and (d(x)y+xd(y)+d(y)x+yd(x))^{n}-(xy+yx) is central for all x,y ∈ I, then R is commutative. We also examine the case where R is a semiprime ring.

참고문헌 (13)

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