TY - JOUR T1 - Annihilators of power values of b-generalized derivations in prime rings AU - Baydar Yarbil, Nihan PY - 2020 DA - December Y2 - 2020 DO - 10.31801/cfsuasmas.628755 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 1278 EP - 1284 VL - 69 IS - 2 LA - en AB - Let $R$ be a prime ring with extended centroid $C$ and maximal left ring of quotients $Q_{ml}(R)$. For a nonzero element $b\in R$ let $F:R\rightarrow R$ be a right generalized $b$-derivation associated with the map $d$ of $R$. Suppose that $s\left(F(x)\right)^n=0$ for all $x\in R$ where $s$ is a nonzero element in $R$ and $n\geq 1$ is a fixed positive integer. Then there exist some $c\in Q{ml}(R)$ and $\beta \in C$ such that $d(x)=ad_c(x)$, $F(x)=(b+\beta)xb$ for all $x\in R$ and either $s(c+\beta)=0$ or $b(c+\beta)=0$. KW - Prime ring KW - generalized polynomial identity CR - Beidar, K. I., Martindale, W. S. III, Mikhalev, A. V., Rings with generalized identities, Marcel Dekker, Inc., New York, xiv+522 pp, 1996. CR - Brešar, M., A note on derivations, Math. J. Okayama Univ., 32 (1990), 83-88. CR - Chang, J.C., Annihilators of power values of a right generalized (α,β)-derivation, Bull. Inst. Math. Acad. Sin., 4 (1) (2009), 67-73. CR - Chuang, C. L., GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc., 103 (3) (1988), 723-728. CR - Erickson, T. S.; Martindale, W. S., 3rd; Osborn, J. M., Prime nonassociative algebras, Pacific J. Math., 60 (1975), No. 1, 49-63. CR - Faith, C., Utumi, Y., On a new proof of Litoff's theorem, Acta Math. Acad. Sci. Hung., 14 (1967), 369-371. CR - Felzenszwalb, B., On a result of Levitzki, Canad. Math. Bull. 21 (2) (1978), 241-242. CR - Giambruno, A., Herstein, I.N., Derivations with nilpotent values, Rend. Circ. Mat. Palermo, 30 (2) (1981), 199-206. CR - Kharchenko,V.K., Differential identities of semiprime rings, Algebra Logika, 18 (1979),86-119; Algebra Logic, (English translation), 18 (1979), 58-80. CR - Kosan, M. T., Lee, T.K., b-generalized derivations having nilpotent values, J. Aust. Math. Soc., 96 (3) (2014), 326-337. CR - Lee, T.K., Lin, J.S., A result on derivations, Proc. Amer. Math. Soc., 124 (1996), 1687-1691. CR - Lee, T. K., Generalized derivations of left faithful rings, Comm. Algebra, 27(8) (1999), 4057-4073. CR - Martindale, W. S. 3rd, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12 (1969), 576-584. UR - https://doi.org/10.31801/cfsuasmas.628755 L1 - https://dergipark.org.tr/en/download/article-file/822835 ER -