Abstract
The purpose of this paper is to study the commutativity of a prime ring
Funding statement: The first author was supported by the National Board for Higher Mathematics (NBHM), India, Grant No. 02011/16/2020 NBHM (R. P.) R & D II/7786.
Acknowledgements
The authors are greatly indebted to the referee for his/her constructive comments and suggestions, which improved the quality of the paper.
References
[1] M. K. Abu Nawas and R. M. Al-Omary, On ideals and commutativity of prime rings with generalized derivations, Eur. J. Pure Appl. Math. 11 (2018), no. 1, 79–89. 10.29020/nybg.ejpam.v11i1.3142Search in Google Scholar
[2] S. Ali, B. Dhara, B. Fahid and M. A. Raza, On semi(prime) rings and algebras with automorphisms and generalized derivations, Bull. Iranian Math. Soc. 45 (2019), no. 6, 1805–1819. 10.1007/s41980-019-00231-5Search in Google Scholar
[3] M. Ashraf, A. Ali and S. Ali, Some commutativity theorems for rings with generalized derivations, Southeast Asian Bull. Math. 31 (2007), no. 3, 415–421. Search in Google Scholar
[4] M. Ashraf and N. U. Rehman, On derivation and commutativity in prime rings, East-West J. Math. 3 (2001), no. 1, 87–91. Search in Google Scholar
[5] M. Ashraf and N. U. Rehman, On commutativity of rings with derivations, Results Math. 42 (2002), no. 1–2, 3–8. 10.1007/BF03323547Search in Google Scholar
[6] K. I. Beidar, W. S. Martindale, III and A. V. Mikhalev, Rings with Generalized Identities, Monogr. Textb. Pure. Appl. Math. 196, Marcel Dekker, New York, 1996. Search in Google Scholar
[7] M. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), no. 2, 385–394. 10.1006/jabr.1993.1080Search in Google Scholar
[8] M. Brešar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), no. 2, 525–546. 10.1090/S0002-9947-1993-1069746-XSearch in Google Scholar
[9] M. Brešar, Commuting maps: A survey, Taiwanese J. Math. 8 (2004), no. 3, 361–397. 10.11650/twjm/1500407660Search in Google Scholar
[10] N. J. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canada Sect. III 49 (1955), 19–22. Search in Google Scholar
[11] I. N. Herstein, Rings with Involution, Chic. Lectures Math., The University of Chicago, Chicago, 1976. Search in Google Scholar
[12] M. Hongan, A note on semiprime rings with derivation, Internat. J. Math. Math. Sci. 20 (1997), no. 2, 413–415. 10.1155/S0161171297000562Search in Google Scholar
[13] J.-S. Lin and C.-K. Liu, Strong commutativity preserving maps on Lie ideals, Linear Algebra Appl. 428 (2008), no. 7, 1601–1609. 10.1016/j.laa.2007.10.006Search in Google Scholar
[14] B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Commutativity theorems in rings with involution, Comm. Algebra 45 (2017), no. 2, 698–708. 10.1080/00927872.2016.1172629Search in Google Scholar
[15] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. 10.1090/S0002-9939-1957-0095863-0Search in Google Scholar
[16] G. S. Sandhu and D. Kumar, A note on derivations and Jordan ideals of prime rings, AIMS Math. 2 (2017), no. 4, 580–585. 10.3934/Math.2017.4.580Search in Google Scholar
[17] J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109 (1990), no. 1, 47–52. 10.1090/S0002-9939-1990-1007517-3Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
