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DERIVATIONS OF PRIME AND SEMIPRIME RINGS
Argac, Nurcan,Inceboz, Hulya G. Korean Mathematical Society 2009 대한수학회지 Vol.46 No.5
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 $\in$ I, then R is commutative. (ii) If char R $\neq$ = 2 and (d(x)y + xd(y) + d(y)x + $yd(x))^n$ - (xy + yx) is central for all x, y $\in$ I, then R is commutative. We also examine the case where R is a semiprime ring.
ON GENERALIZED (σ, τ)-DERIVATIONS II
Argac, Nurcan,Inceboz, Hulya G. Korean Mathematical Society 2010 대한수학회지 Vol.47 No.3
This paper continues a line investigation in [1]. Let A be a K-algebra and M an A/K-bimodule. In [5] Hamaguchi gave a necessary and sufficient condition for gDer(A, M) to be isomorphic to BDer(A, M). The main aim of this paper is to establish similar relationships for generalized ($\sigma$, $\tau$)-derivations.
ON GENERALIZED (σ,ι)-DERIVATIONS Ⅱ
Raluca Mocanu,Hulya G. Inceboz 대한수학회 2010 대한수학회지 Vol.47 No.3
This paper continues a line investigation in [1]. Let A be a K-algebra and M an A/K-bimodule. In [5] Hamaguchi gave a necessary and sufficient condition for gDer(A,M) to be isomorphic to BDer(A,M). The main aim of this paper is to establish similar relationships for generalized (σ,ι)-derivations.
Derivations of prime and semiprime rings
Nurcan Argac,Hulya G. Inceboz 대한수학회 2009 대한수학회지 Vol.46 No.5
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. 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.