Centrally-extended generalized Jordan derivations in rings
Keywords:
Associative rings, involution, generalized Jordan derivation, centrally extended generalized Jordan derivationAbstract
In this article, we introduce the notion of centrally-extended generalized Jordan derivations and characterize the structure of a prime ring (resp. *-prime ring) R that admits a centrally-extended generalized Jordan derivation F satisfying [F(x), x] ∈ Z(R) (resp. [F(x), x*] ∈ Z(R)) for all x ∈ R.
References
Ali, Shakir, and Nadeem Ahmad Dar. "On *-centralizing mappings in rings with involution." Georgian Math. J. 21, no. 1 (2014): 25-28.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Ashraf, Mohammad, Shakir Ali, and Claus Haetinger. "On derivations in rings and their applications." Aligarh Bull. Math. 25, no. 2 (2006): 79-107.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Beidar, Konstantin Igorevich, Wallace Smith Martindale III, and Aleksandr Vasil'evich Mikhalev. Rings with Generalized Identities. Vol. 196 of Pure ppl.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Math. New York: Marcel Dekker Inc., 1996.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bell, Howard Edwin, and Mohamad Nagy Daif. "On centrally-extended maps on rings." Beitr. Algebra Geom. 57, no. 1 (2016): 129-136.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Bhushan, Bharat, Gurninder Singh Sandhu, Shakir Ali, and Deepak Kumar. "On centrally extended Jordan derivations and related maps in rings." Hacet. J. Math. Stat. 52, no. 1 (2023): 23-35.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Brešar, Matej. "Jordan derivations on semiprime rings." Proc. Amer. Math. Soc. 104, no. 4 (1988): 1003-1006.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Brešar, Matej. "On the distance of the composition of two derivations to the generalized derivations." Glasgow Math. J. 33, no. 1 (1991): 89-93.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Brešar, Matej. "Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings." Trans. Amer. Math. Soc. 335, no. 2 (1993): 525-546.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Brešar, Matej. "Centralizing mappings and derivations in prime rings." J. Algebra 156, no. 2 (1993): 385-394.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Macedo Ferreira, Bruno Leonardo, Ruth Nascimento Ferreira, and Henrique Guzzo. "Generalized Jordan derivations on semiprime rings." J. Aust. Math. Soc. 109, no. 1 (2020): 36-43.
##plugins.generic.googleScholarLinks.settings.viewInGS##
De Filippis, Vincenzo. "Generalized derivations and commutators with nilpotent values on Lie ideals." Tamsui Oxf. J. Math. Sci. 22, no. 2 (2006): 167-175.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Herstein, Israel Nathan. "Jordan derivations of prime rings." Proc. Amer. Math. Soc. 8 (1957): 1104-1110.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Jing, Wu, and Shi Jie Lu. "Generalized Jordan derivations on prime rings and standard operator algebras." Taiwanese J. Math. 7, no. 4 (2003): 605-613.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lee, Tsiu-Kwen. "Generalized derivations of left faithful rings." Comm. Algebra27, no. 8 (1999): 4057-4073.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Lee, Pjek Hwee, and Tsiu-Kwen Lee. "Derivations centralizing symmetric or skew elements." Bull. Inst. Math. Acad. Sinica 14, no. 3 (1986): 249-256.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Martindale, Wallace Smith, III. "Prime rings with involution and generalized polynomial identities." J. Algebra 22 (1972): 502-516.
##plugins.generic.googleScholarLinks.settings.viewInGS##
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