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Original Articles

Lie n-derivations of incidence algebras

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Pages 105-118 | Received 23 Apr 2019, Accepted 04 Jun 2019, Published online: 02 Jul 2019

References

  • Abdullaev, I. Z. (1992). n-Lie derivations on von Neumann algebras. Uzbek. Math. J. 5–6: 3–9.
  • Baclawski, K. (1972). Antomorphisms and derivations of incidence algebras. Proc. Amer. Math. Soc. 36(2): 351–356. DOI:10.2307/2039158.
  • Benkovič, D., Eremita, D. (2012). Multiplicative Lie n-derivations of triangular rings. Linear Algebra Appl. 436(11):4223–4240. DOI:10.1016/j.laa.2012.01.022.
  • Brešar, M. (1993). Commuting traces of biadditive mappings, commutativity-preserving mappings and lie mappings. Trans. Amer. Math. Soc. 335(2): 525–546. DOI:10.1090/S0002-9947-1993-1069746-X.
  • Brešar, M. (2004). Commuting maps: A survey. Taiwan. J. Math. 8: 361–397.
  • Brusamarello, R., Lewis, D. (2011). Automorphisms and involutions on incidence algebras. Linear Multilinear Algebra 59(11): 1247–1267. DOI:10.1080/03081087.2010.496113.
  • Fošner, A., Wei, F., Xiao, Z.-K. (2013). Nonlinear lie-type derivations of von Neumann algebras and related topics. Colloq. Math. 132(1): 53–71. DOI:10.4064/cm132-1-5.
  • Herstein, I. N. (1961). Lie and Jordan structures in simple, associative rings. Bull. Amer. Math. Soc. 67(6): 517–531. DOI:10.1090/S0002-9904-1961-10666-6.
  • Kaygorodov, I., Khrypchenko, M., Wei, F. (2018). Higher derivations of finitary incidence algebras. Algebras Represent. Theory. DOI:10.1007/s10468-018-9822-4.
  • Khrypchenko, M. (2016). Jordan derivations of finitary incidence rings. Linear Multilinear Algebra 64(10): 2104–2118. DOI:10.1080/03081087.2016.1139036.
  • Khrypchenko, M. (2018). Local derivations of finitary incidence rings. Acta Math. Hungar. 154(1): 48–55. DOI:10.1007/s10474-017-0758-7.
  • Khrypchenko, M., Wei, F. (2019). Lie-type derivations of finitary incidence algebras. arXiv[math.RA]:1902.04338.
  • Koppinen, M. (1995). Automorphisms and higher derivations of incidence algebras. J. Algebra 174(2): 698–723. DOI:10.1006/jabr.1995.1147.
  • Martindale, W. S., III. (1964). Lie derivations of primitive rings. Michigan Math. J. 11: 183–187. DOI:10.1307/mmj/1028999091.
  • Qi, X.-F. (2015). Characterizing Lie n-derivations for reflexive algebras. Linear Multilinear Algebra 63(8): 1693–1706. DOI:10.1080/03081087.2014.968519.
  • Qi, X.-F. (2017). Lie n-derivations on J-subspace lattice algebras. Proc. Math. Sci. 127: 537–545. DOI:10.1007/s12044-017-0340-9.
  • Spiegel, E. (2001). On the automorphisms of incidence algebras. J. Algebra 239(2): 615–623. DOI:10.1006/jabr.2000.8702.
  • Spiegel, E., O’Donnell, C. (1997). Incidence Algebras, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 206. New York, NY: Marcel Dekker.
  • Stanley, R. (1970). Structure of incidence algebras and their automorphism groups. Bull. Amer. Math. Soc. 76(6): 1236–1239. DOI:10.1090/S0002-9904-1970-12617-9.
  • Stanley, R. (1997). Enumerative Combinatorics I, with a Foreword by Gian-Carlo Rota. Cambridge Studies in Advanced Mathematics, Vol. 49. Cambridge: Cambridge University Press.
  • Wang, D.-N., Xiao, Z.-K. (2019). Lie triple derivations of incidence algebras. Commun. Algebra. 47(5): 1841–1852. DOI:10.1080/00927872.2018.1523422.
  • Wang, Y. (2014). Lie n-derivations of unital algebras with idempotents. Linear Algebra Appl. 458: 512–525. DOI:10.1016/j.laa.2014.06.029.
  • Wang, Y., Wang, Y. (2013). Multiplicative Lie n-derivations of generalized matrix algebras. Linear Algebra Appl. 438(5): 2599–2616. DOI:10.1016/j.laa.2012.10.052.
  • Ward, M. (1937). Arithmetic functions on rings. Ann. Math. 38(3): 725–732. DOI:10.2307/1968611.
  • Xiao, Z.-K. (2015). Jordan derivations of incidence algebras. Rocky Mt. J. Math. 45(4): 1357–1368. DOI:10.1216/RMJ-2015-45-4-1357.
  • Zhang, X., Khrypchenko, M. (2017). Lie derivations of incidence algebras. Linear Algebra Appl. 513: 69–83. DOI:10.1016/j.laa.2016.10.011.

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