211
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Lie Centralizers and generalized Lie derivations on prime rings by local actions

& ORCID Icon
Pages 5277-5286 | Received 14 Sep 2022, Accepted 11 Jun 2023, Published online: 28 Jun 2023

References

  • Alaminos, J., Extremera, J., Villena, A. R., Brešar, M. (2007). Characterizing homomorphisms and derivations on c*-algebras. Proc. Royal Soc. Edinburgh Sec. A: Math. 137(1):1–7. DOI: 10.1017/S0308210505000090.
  • Behfar, R., Ghahramani, H. (2021). Lie maps on triangular algebras without assuming unity. Mediterr. J. Math. 18:1–28. DOI: 10.1007/s00009-021-01836-z.
  • Martindale, W. S., Beidar, K. I., Mikhalev, A. V. (1996). Rings with Generalized Identities. Pure and Applied Mathematics. New York: Dekker.
  • Benkovič, D. (2019). Generalized lie n-derivations of triangular algebras. Commun. Algebra 147(12):5294–5302. DOI: 10.1080/00927872.2019.1617875.
  • Brešar, M. (2007). Characterizing homomorphisms, derivations and multipliers in rings with idempotents. Proc. Royal Soc. Edinburgh Sec. A: Math. 137(1):9–21. DOI: 10.1017/S0308210504001088.
  • Brešar, M., Chebotar, M. A., Martindale, W. S. (2007). Functional identities. Basel: Springer.
  • Chebotar, M. A., Ke, W.-F., Lee, P.-H. (2004). Maps characterized by action on zero products. Pac. J. Math. 216(2):217–228. DOI: 10.2140/pjm.2004.216.217.
  • Fadaee, B., Ghahramani, H. (2020). Linear maps on c-algebras behaving like (anti-) derivations at orthogonal elements. Bull. Malaysian Math. Sci. Soc. 43(3):2851–2859.
  • Fadaee, B., Ghahramani, H. (2022). Lie centralizers at the zero products on generalized matrix algebras. J. Algebra Appl. 21(8):2250165. DOI: 10.1142/S0219498822501651.
  • Fadaee, B., Ghahramani, H. (2018). Jordan left derivations at the idempotent elements on reflexive algebras. Publ. Math. Debrecen 92(3–4):261–275. DOI: 10.5486/PMD.2018.7785.
  • Fadaee, B., Ghahramani, H., Jing, W. (2022). Lie triple centralizers on generalized matrix algebras. Quaest. Math. 1–20.
  • Fošner, A., Jing, W. (2019). Lie centralizers on triangular rings and nest algebras. Adv. Operator Theory 4(2): 342–350. DOI: 10.15352/aot.1804-1341.
  • Fošner, A., Wei, F., Xiao, Z. (2013). Nonlinear lie-type derivations of von neumann algebras and related topics. Colloq. Math. 1:53–71. DOI: 10.4064/cm132-1-5.
  • Ghahramani, H. (2012). Additive mappings derivable at non-trivial idempotents on banach algebras. Linear Multilinear Algebra 60(6):725–742. DOI: 10.1080/03081087.2011.628664.
  • Ghahramani, H. (2018). Characterizing jordan maps on triangular rings through commutative zero products. Mediterr. J. Math. 15:1–10. DOI: 10.1007/s00009-018-1082-3.
  • Ghahramani, H., Jing, W. (2021). Lie centralizers at zero products on a class of operator algebras. Ann. Funct. Anal. 12:1–12. DOI: 10.1007/s43034-021-00123-y.
  • Jabeen, A. (2021). Lie (jordan) centralizers on generalized matrix algebras. Commun. Algebra 49(1):278–291. DOI: 10.1080/00927872.2020.1797759.
  • Jacobson, N. (1979). Lie Algebras, no. 10. North Chelmsford, MA: Courier Corporation.
  • Ji, P., Qi, W., Sun, X. (2013). Characterizations of lie derivations of factor von neumann algebras. Linear Multilinear Algebra 61(3):417–428. DOI: 10.1080/03081087.2012.689982.
  • Jing, W., Lu, S., Li, P. (2002). Characterisations of derivations on some operator algebras. Bull. Austral. Math. Soc. 66(2):227–232. DOI: 10.1017/S0004972700040077.
  • Lin, W. (2018). Nonlinear generalized lie n-derivations on triangular algebras. Commun. Algebra 46(6):2368–2383. DOI: 10.1080/00927872.2017.1383999.
  • Liu, L. (2022). On nonlinear lie centralizers of generalized matrix algebras. Linear Multilinear Algebra 70(14): 2693–2705. DOI: 10.1080/03081087.2020.1810605.
  • Lu, F., Jing, W. (2010). Characterizations of lie derivations of b (x). Linear Algebra Appl. 432(1):89–99. DOI: 10.1016/j.laa.2009.07.026.
  • McCrimmon, K. (2004). A Taste of Jordan Algebras, Vol. 1. New York: Springer.
  • Qi, X., Hou, J. (2011). Characterization of lie derivations on prime rings. Commun. Algebra 39(10):3824–3835. DOI: 10.1080/00927872.2010.512588.
  • 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.
  • Zhu, J., Zhao, S. (2013). Characterizations of all-derivable points in nest algebras. Proc. Amer. Math. Soc. 141(7):2343–2350. DOI: 10.1090/S0002-9939-2013-11511-X.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.