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Keywords:
derivation; generalized derivation; $*$-Jordan ideal; commutativity theorems
derivation; generalized derivation; $*$-Jordan ideal; commutativity theorems
Summary:
In this paper we investigate commutativity of ring $R$ with involution $'\ast'$ which admits a derivation satisfying certain algebraic identities on Jordan ideals of $R$. Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
References:
[1] Awtar R.: Lie and Jordan structure in prime rings with derivations. Proc. Amer. Math. Soc. 41 (1973), 67–74. DOI 10.1090/S0002-9939-1973-0318233-5 | MR 0318233 | Zbl 0271.16016
[2] Bell H.E., Daif M.N.: On derivations and commutativity in prime rings. Acta Math. Hungar. 66 (1995), 337–343. DOI 10.1007/BF01876049 | MR 1314011 | Zbl 0822.16033
[3] Daif M.N., Bell H.E.: Remarks on derivations on semiprime rings. Internat. J. Math. Math. Sci. 15 (1992), 205–206. DOI 10.1155/S0161171292000255 | MR 1143947 | Zbl 0746.16029
[4] Herstein I.N.: Rings with Involution. Univ. Chicago Press, Chicago, 1976. MR 0442017 | Zbl 0495.16007
[5] Herstein I.N.: A note on derivations. Canad. Math. Bull. 21 (1978), 369–370. DOI 10.4153/CMB-1978-065-x | MR 0506447 | Zbl 0434.16027
[6] Hongan M.: A note on semiprime rings with derivation. Internat. J. Math. Math. Sci. 20 (1997), no. 2, 413–415. DOI 10.1155/S0161171297000562 | MR 1444747 | Zbl 0879.16025
[7] Mamouni A., Oukhtite L.: Derivations satisfying certain algebraic identities on Jordan ideals. Arab. J. Math. 1 (2012), no. 3, 341–346. DOI 10.1007/s40065-012-0039-9 | MR 3041071
[8] Mamouni A., Oukhtite L.: Generalized derivations centralizing on Jordan ideals of rings with involution. submitted.
[9] Oukhtite L.: On Jordan ideals and derivations in rings with involution. Comment. Math. Univ. Carolin. 51 (2010), no. 3, 389–395. MR 2741872 | Zbl 1211.16037
[10] Oukhtite L.: Posner's second theorem for Jordan ideals in rings with involution. Expo. Math. 29 (2011), 415–419. DOI 10.1016/j.exmath.2011.07.002 | MR 2861767 | Zbl 1232.16027
[11] Oukhtite L., Salhi S.: On derivations in $\sigma$-prime rings. Int. J. Algebra 1 (2007), no. 5, 241–246. MR 2342997 | Zbl 1124.16025
[12] Zaidi S.M.A., Ashraf A., Ali S.: On Jordan ideals and left $(\theta ,\theta)$-derivations in prime rings. Int. J. Math. Math. Sci. 2004, no. 37–40, 1957–1964. DOI 10.1155/S0161171204309075 | MR 2100888 | Zbl 1069.16041
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