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• W2093689621 abstract "Let K be a commutative ring with unit, R be a prime K-algebra with center Z(R), right Utumi quotient ring U and extended centroid C, and I a nonzero right ideal of R. Let g be a nonzero generalized derivation of R and f(X 1 ,…,X n ) a multilinear polynomial over K. If g(f(x 1 ,…,x n )) f(x 1 ,…,x n ) ∈ C for all x 1 ,…,x n ∈ I, then either f(x 1 ,…,x n )x n+1 is an identity for I, or char (R)=2 and R satisfies the standard identity s 4 (x 1 ,…,x 4 ), unless when g(x)=ax+[x,b] for suitable a, b ∈ U and one of the following holds: (i) a, b ∈ C and f(x 1 ,…,x n ) 2 is central valued on R; (ii) a ∈ C and f(x 1 ,…,x n ) is central valued on R; (iii) aI=0 and [f(x 1 ,…,x n ), x n+1 ]x n+2 is an identity for I; (iv) aI=0 and (b-β)I=0 for some β ∈ C." @default.
• W2093689621 created "2016-06-24" @default.
• W2093689621 creator A5031366335 @default.
• W2093689621 creator A5041821766 @default.
• W2093689621 date "2011-12-01" @default.
• W2093689621 modified "2023-10-16" @default.
• W2093689621 title "Prime Rings with Generalized Derivations on Right Ideals" @default.
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• W2093689621 doi "https://doi.org/10.1142/s1005386711000861" @default.
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