We study some properties of centralizing and strong commutativity preserving maps of semiprime rings.
References
A. Ali, M. Yasen, and M. Anwar, “Strong commutativity preserving mappings on semiprime rings,” Bull. Korean Math. Soc., 43, No. 4, 711–713 (2006).
M. Ashraf and N. Rehman, “On derivations and commutativity in prime rings,” East-West J. Math., 3, No. 1, 87–91 (2001).
M. Ashraf, A. Asma, and A. Shakir, “Some commutativity theorems for rings with generalized derivations,” Southeast Asain Bull. Math., 31, 415–421 (2007).
H. E. Bell and W. S. Martindale, “Centralizing mappings of semiprime rings,” Can. Math. Bull., 30, 92–101 (1987).
H. E. Bell and M. N. Daif, “On commutativity and strong commutativity preserving maps,” Can. Math. Bull., 37, No. 4, 443–447 (1994).
M. Bresar, “Centralizing mappings and derivations in prime rings,” J. Algebra, 156, 385–394 (1993).
M. Bresar, “Commuting traces of biadditive mappings, commutativity preserving mappings, and Lie mappings,” Trans. Amer. Math. Soc., 335, No. 2, 525–546 (1993).
M. A. Chaudhry and A. B. Thaheem, “Centralizing mappings and derivations on semiprime rings,” Demonstr. Math., 37, No. 2, 285–292 (2004).
M. N. Daif and H. E. Bell, “Remarks on derivations on semiprime rings,” Int. J. Math. and Math. Sci., 15, No. 1, 205–206 (1992).
J. Ma and X. W. Xu, “Strong commutativity-preserving generalized derivations on semiprime rings,” Acta Math. Sinica (English Ser.), 24, No. 11, 1835–1842 (2008).
J. H. Mayne, “Centralizing automorphisms of prime rings,” Can. Math. Bull., 19, 113–115 (1976).
A. B. Thaheem and M. S. Samman, “Centralizing mappings on semiprime rings,” Int. J. Pure Appl. Math., 3, 249–254 (2002).
M. S. Samman, “On strong commutativity-preserving maps,” Int. J. Math. Math. Sci., 6, 917–923 (2005).
E. C. Posner, “Derivations in prime rings,” Proc. Amer. Math. Soc., 8, 1093–1100 (1957).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 2, pp. 279–285, February, 2015.
Rights and permissions
About this article
Cite this article
Huang, S., Göbaşı, Ö. & Koç, E. On Centralizing and Strong Commutativity Preserving Maps of Semiprime Rings. Ukr Math J 67, 323–331 (2015). https://doi.org/10.1007/s11253-015-1082-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-015-1082-4