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On (m, n)-derivations of some algebras

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Abstrakty
EN
Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A + nBδ(A) for all A, B (…) A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA (…) 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.
Wydawca
Rocznik
Strony
672--694
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • School of Mathematics and Information, Shanghai Lixin University of Commerce, Shanghai, 201620, Pr China
autor
  • Department of Mathematics, East China University of Science and Technology, Shanghai 200237, Pr China
autor
  • Department of Mathematics, East China University of Science and Technology, Shanghai 200237, Pr China
Bibliografia
  • [1] J. Alaminos, M. Mathieu, A. Villena, Symmetric amenability and Lie derivations, Math. Proc. Cambridge Philos. Soc. 137 (2004), 433–439.
  • [2] R. An, J. Hou, Characterization of derivations on triangular rings: additive maps derivable at idempotents, Linear Algebra Appl. 431 (2009), 1070–1080.
  • [3] R. An, J. Hou, Characterizations of Jordan derivations on rings with idempotent, Linear Multilinear Algebra 58 (2010), 753–763.
  • [4] M. Brešar, Characterizing homomorphisms, derivations and multipliers in rings with idempotents, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 9–21.
  • [5] M. Brešar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003–1006.
  • [6] W. Cheung, Lie derivations of triangular algebra, Linear Multilinear Algebra 51 (2003), 299–310.
  • [7] K. Davidson, Nest Algebras, Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, 1988.
  • [8] I. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104–1110.
  • [9] J. Hou, R. An, Additive maps on rings behaving like derivations at idempotent-product elements, J. Pure Appl. Algebra. 215 (2011), 1852–1862.
  • [10] J. Hou, X. Qi, Additive maps derivable at some points on J-subspace lattice algebras, Linear Algebra Appl. 429 (2008), 1851–1863.
  • [11] M. Jiao, J. Hou, Additive maps derivable or Jordan derivable at zero point on nest algebras, Linear Algebra Appl. 432 (2010), 2984–2994.
  • [12] B. Johnson, Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. Proc. Cambridge Philos. Soc. 120 (1996), 455–473.
  • [13] J. Li, Z. Pan, Annihilator-preserving maps, multipliers, and derivations, Linear Algebra Appl. 432 (2010), 5–13.
  • [14] J. Li, Z. Pan, On derivable mappings, J. Math. Anal. Appl. 374 (2011), 311–322.
  • [15] J. Li, Z. Pan, H. Xu, Characterizations of isomorphisms and derivations of some algebras, J. Math. Anal. Appl. 332 (2007), 1314–1322.
  • [16] F. Lu, J. Wu, Characterizations of Lie derivations of B(X), Linear Algebra Appl. 432 (2010), 89–99.
  • [17] F. Lu, Characterizations of derivations and Jordan derivations on Banach algebras, Linear Algebra Appl. 430 (2009), 2233–2239.
  • [18] F. Lu, The Jordan structure of CSL algebras, Studia Math. 190 (2009), 283–299. [19] X. Qi, J. Hou, Characterizations of derivations of Banach space nest algebras: allderivable point, Linear Algebra Appl. 432 (2010), 3183–3200.
  • [20] A. Sands, Radicals and Morita contexts, J. Algebra 24 (1973), 335–345.
  • [21] J. Vukman, On pm; nq-Jordan derivation and commutativity of prime rings, Demonstratio Math. 41 (2008), 773–778.
  • [22] J. Zhang, W. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl. 419 (2006), 251–255.
  • [23] S. Zhao, J. Zhu, Jordan all-derivable points in the algebra of all upper triangular matrices, Linear Algebra Appl. 433 (2010), 1922-1938.
  • [24] J. Zhu, C. Xiong, All-derivable points in continuous nest algebras, J. Math. Anal. Appl. 340 (2008), 843–853.
  • [25] J. Zhu, C. Xiong, Derivable mappings at unit operator on nest algebras, Linear Algebra Appl. 422 (2007), 721–735.
  • [26] J. Zhu, C. Xiong, R. Zhang, All-derivable points in the algebra of all upper triangular matrices, Linear Algebra Appl. 429(4) (2008), 804–818.
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Bibliografia
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