Bi-additive maps of ξ-Lie product type vanishing on zero products of XY and YX

References

• Alaminos, J., Brešar, M., Extremera, J., Villena, A. R. (2010). Characterizing Jordan maps on C*-algebras through zero products. Proc. Edinburgh Math. Soc. 53(3):543–555.
   Web of Science ®Google Scholar
• Alaminos, J., Brešar, M., Extremera, J., Villena, A. R. (2010). On bilinear maps determined by rank one idempotents. Linear Algebra Appl. 432(2–3):738–743.
   Web of Science ®Google Scholar
• Amitsur, S. A. (1982). Extension of derivations to central simple algebras. Commun. Algebra 10(8):797–803.
   Web of Science ®Google Scholar
• Araujo, J., Jarosz, K. (2003). Biseparating maps between operator algebras. J. Math. Anal. Appl. 282(1):48–55.
   Web of Science ®Google Scholar
• Beidar, K. I., Martindale, W. S. 3rd. (1998). On functional identities in prime rings with involution. J. Algebra 203(2):491–532.
   Web of Science ®Google Scholar
• Beidar, K. I., Martindale, W. S. 3rd (1996). Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 196. New York: Marcel Dekker, Inc.
   Google Scholar
• Brešar, M. (1992). Characterizations of derivations on some normed algebras with involution. J. Algebra 152:454–462.
   Web of Science ®Google Scholar
• Brešar, M. (2007). Characterizing homomorphisms, multipliers and derivations in rings with idempotents. Proc. R. Soc. Edinburgh Sect. A. 137:9–21.
   Web of Science ®Google Scholar
• Brešar, M. (2012). Multiplication algebra and maps determined by zero products. Linear Multilinear Algebra 60(7):763–768.
   Web of Science ®Google Scholar
• Brešar, M., Chebotar, M. A., Martindale, W. S. III. (2007). Functional Identities, Frontiers in Mathematics. Basel: Birkhauser Verlag.
   Google Scholar
• Brešar, M., Grašič, M., Sanchez, J. (2009). Zero product determined matrix algebras. Linear Algebra Appl. 430:1486–1498.
   Web of Science ®Google Scholar
• Brešar, M., Grašič, M., Sanchez, J. (2010). Zero product determined matrix algebras. In: Proceedings of Jordan Structures in Algebra and Analysis Meeting, 49–63, Editorial Circulo Rojo, Almeria.
   Google Scholar
• Brooke, J. A., Busch, P., Pearson, D. B. (2002). Commutativity up to a factor of bounded operators in complex Hilbert space. R. Soc. London Proc. Ser. A Math. Phys. Eng. Sci. 458(2017):109–118.
   Web of Science ®Google Scholar
• Chebotar, M. A., Ke, W.-F., Lee, P.-H. (2004). Characterized by action on zero products. Pacific J. Math. 216(2):217–228.
   Web of Science ®Google Scholar
• Chebotar, M. A., Ke, W.-F., Lee, P.-H. (2005). Maps preserving zero Jordan products on Hermitian operators. Illinois J. Math. 49(2):445–452.
   Google Scholar
• Chen, Y., Li, J. (2011). Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products. Studia Math. 206(2):121–134.
   Web of Science ®Google Scholar
• Chuang, C.-L. (1988). GPIs having coefficients in Utumi quotient rings. Proc. Am. Math. Soc. 103(3):723–728.
   Web of Science ®Google Scholar
• Chuang, C.-L., Lee, T.-K. (2011). Derivations modulo elementary operators. J. Algebra 338:56–70.
   Web of Science ®Google Scholar
• Cui, J. L., Hou, J., Park, C. (2008). Additive maps preserving commutativity up to a factor. Chinese Ann. Math. Ser. A 29(5):583–590.
   Google Scholar
• Ghahramani, H. (2013). Zero product determined some nest algebras. Linear Algebra Appl. 438(1):303–314.
   Web of Science ®Google Scholar
• Ghosseiri, N. M. (2007). Jordan derivations of some classes of matrix rings. Taiwanese J. Math. 11(1):51–62.
   Web of Science ®Google Scholar
• Grašič, M. (2011). Zero product determined Jordan algebras, I. Linear Multilinear Algebra 59(6):671–685.
   Web of Science ®Google Scholar
• Herstein, I. N. (1969). Topics in Ring Theory. Chicago, Ill.-London: The University of Chicago Press.
   Google Scholar
• Jacobson, N., Rickart, C. (1950). Jordan homomorphisms of rings. Trans. Am. Math. Soc. 69:479–502.
   Web of Science ®Google Scholar
• Jing, W., Lu, S., Li, P. (2002). Characterisations of derivations on some operator algebras. Bull. Austral. Math. Soc. 66:227–232.
   Web of Science ®Google Scholar
• Kassel, C. (1995). Quantum Groups. New York: Springer-Verlag.
   Google Scholar
• Koşan, M. T., Lee, T.-K., Zhou, Y. (2014). Bilinear forms on matrix algebras vanishing on zero products of xy and yx. Linear Algebra Appl. 453:110–124.
   Web of Science ®Google Scholar
• Lee, T.-K. (1992). Semiprime rings with differential identities. Bull. Inst. Math. Acad. Sinica 20:27–38.
   Google Scholar
• Lee, T.-K. (1995). A note on rings without nonzero nil one-sided ideals. Chinese J. Math. 23(4):383–385.
   Google Scholar
• Lee, T.-K. (2004). Generalized skew derivations characterized by acting on zero products. Pacific J. Math. 216(2):293–301.
   Web of Science ®Google Scholar
• Qi, X., Cui, J., Hou, J. (2011). Characterizing additive ξ-Lie derivations of prime algebras by ξ-Lie zero products. Linear Algebra Appl. 434(3):669–682.
   Web of Science ®Google Scholar
• Qi, X., Hou, J. (2009). Additive Lie (ξ-Lie) derivations and generalized Lie (ξ-Lie) derivations on nest algebras. Linear Algebra Appl. 431(5–7):843–854.
   Web of Science ®Google Scholar
• Qi, X., Hou, J. (2011). Characterization of Lie derivations on prime rings. Commun. Algebra 39(10):3824–3835.
   Web of Science ®Google Scholar
• Qi, X., Hou, J. (2011). Generalized skew derivations on nest algebras characterized by acting on zero products. Publ. Math. Debrecen 78(2):457–468.
   Web of Science ®Google Scholar
• Rowen, L. (1973). Some results on the center of a ring with polynomial identity. Bull. Am. Math. Soc. 79:219–223.
   Web of Science ®Google Scholar
• Zhao, L., Hou, J. (2006). Jordan zero-product preserving additive maps on operator algebras. J. Math. Anal. Appl. 314(2):689–700.
   Web of Science ®Google Scholar