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Characterization of jordan*-derivations by local action on rings with involution | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 2، اسفند 2017، صفحه 120-127 اصل مقاله (264.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2666 | ||
| نویسندگان | ||
| Xingxing Zhao* ؛ Xiaofei Qi | ||
| Department of Mathematics, Shanxi University, Taiyuan, China | ||
| چکیده | ||
| Let R be a ring with an involution ∗ and a symmetric idempotent e. It is shown that, under some mild conditions on R, an additive map δ : R → R satisfies δ(ab + ba) = δ(a)b ∗ + aδ(b) + δ(b)a ∗ + bδ(a) whenever ab = e for a, b ∈ R if and only if δ is a Jordan *-derivation. | ||
| کلیدواژه‌ها | ||
| Rings with involution؛ Jordan *-derivations؛ Derivations | ||
| مراجع | ||
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[1] M. Breˇsar, M. A. Chebotar and W. S. Martindale III, Functional identities,Birkh¨auser Basel: (2006). [2] M. Bresar, Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. R. Soc. Edinb. Sect. A, 137 (2007), 9-21. [3] M. Breˇsar and J. Vukman, On some additive mappings in rings with involution, Aequationes Math., 38 (1989), 178-185. [4] C.-L. Chuang, A. Foˇsner and T.-K. Lee, Jordan τ -derivations of locally matrix rings, Algebra Represent. Theory, 16 (2013), 755-763. [5] A. Foˇsner and T.-K.Lee, Jordan *-derivations of finite-dimensional semiprime algebras, Canad.Math.Bull.,57(2014),51-60. [6] J.-C. Hou and X.-F. Qi, Additive maps derivable at some points on J -subspace lattice algebras, Linear Algebra Appl., 429 (2008), 1851-1863. [7] S. Kurepa, Quadratic and sesquilinear functionals, Glasg. Math. J., 20 (1965),79-92. [8] T.-K. Lee and Y.-Q. Zhou, Jordan *-derivations of prime rings, J. Algebra Appl.,13 (2014), 1350126. [9] T.-K. Lee, T.-L. Wong and Y. Zhou, The structure of Jordan *-derivations of prime rings, Linear Multilinear Algebra, 63 (2015), 411-422. [10] X.-F. Qi and F.-F. Zhang, Multiplicative Jordan *-derivations on rings with in-volution, Linear Multilinear Algebra, 64 (2016), 1145-1162. [11] P. Semrl, ˇ Quadratic functionals and Jordan *-derivations, Studia Math., 97 (1991), 157-165. [12] P. Semrl, ˇ Quadratic and quasi-quadratic functionals, Proc. Amer. Math. Soc.,119 (1993), 1105-1113. [13] P. Semrl, ˇ Jordan *-derivations of standard operator algebras, Proc. Amer. Math.Soc., 120 (1994), 515-518. [14] J. Vukman, Some functional equations in Banach algebras and an application,Proc. Amer.Math. Soc.,100(1987),133-136. [15] F.-F. Zhang and X.-F. Qi, Characterizing local Jordan *-derivations on rings with involution, submitted. | ||
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