427
Views
5
CrossRef citations to date
0
Altmetric
Articles

Herstein’s theorem for prime ideals in rings with involution involving pair of derivations

, ORCID Icon &
Pages 2592-2603 | Received 05 Oct 2021, Accepted 18 Nov 2021, Published online: 05 Jan 2022

References

  • Ali, S., Dar, N. A. (2014). On *-centralizing mappings in rings with involution. Georgian Math. J. 21(1):25–28.
  • Ali, S., Shuliang, H. (2012). On derivations in semiprime rings. Algebr. Represent. Theory 15(6):1023–1033. DOI: 10.1007/s10468-011-9271-9.
  • Ali, S., Dar, N. A., Khan, A. N. (2015). On strong commutativity preserving like maps in rings with involution. Miskolc Math. Notes 16(1):17–24. DOI: 10.18514/MMN.2015.1297.
  • Ashraf, M., Rehman, N. (2002). On commutativity of rings with derivations. Results Math. 42(1–2):3–8. DOI: 10.1007/BF03323547.
  • Bell, H. E., Daif, M. N. (1994). On commutativity and strong commutativity-preserving maps. Canad. Math. Bull. 37(4):443–447. DOI: 10.4153/CMB-1994-064-x.
  • Daif, M. N. (1998). Commutativity results for semiprime rings with derivations. Int. J. Math. Math. Sci. 21(3):471–474. DOI: 10.1155/S0161171298000660.
  • Dar, N. A., Ali, S. (2016). On *-commuting mappings and derivations in rings with involution. Turkish J. Math. 40(4):884–894.
  • Deng, Q., Ashraf, M. (1996). On strong commutativity preserving mappings. Results Math. 30(3–4):259–263. DOI: 10.1007/BF03322194.
  • Herstein, I. N. (1978). A note on derivations. Canad. Math. Bull. 21(3):369–370. DOI: 10.4153/CMB-1978-065-x.
  • Herstein, I. N. (1976). Rings with Involution. Chicago: University of Chicago Press.
  • Lanski, C. (1988). Differential identities, Lie ideals, and Posner’s theorems. Pacific J. Math. 134(2):275–297. DOI: 10.2140/pjm.1988.134.275.
  • Mamouni, A., Nejjar, B., Oukhtite, L. (2018). Differential identities on prime rings with involution. J. Algebra Appl. 17(9):1850163. DOI: 10.1142/S0219498818501633.
  • Mamouni, A., Oukhtite, L., Zerra, M. (2020). On derivations involving prime ideals and commutativity in rings. São Paulo J. Math. Sci. 14(2):675–688. DOI: 10.1007/s40863-020-00187-z.
  • Mir, H. E., Mamouni, A., Oukhtite, L. (2020). Commutativity with algebraic identities involving prime ideals. Commun. Korean Math. Soc. 35(3):723–731.
  • Nejjar, B., Kacha, A., Mamouni, A., Oukhtite, L. (2017). Commutativity theorems in rings with involution. Commun. Algebra 45(2):698–708. DOI: 10.1080/00927872.2016.1172629.
  • Posner, E. C. (1957). Derivations in prime rings. Proc. Amer. Math. Soc. 8(6):1093–1100. DOI: 10.1090/S0002-9939-1957-0095863-0.

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.