Skip to main content
SpringerLink
Log in

Some results involving P-derivations and prime ideals in rings

  • Published:
ANNALI DELL'UNIVERSITA' DI FERRARA Aims and scope Submit manuscript

Abstract

Let R be any arbitrary associative ring and P be a prime ideal of R. In this article, we define and study the notion of P-derivation, generalized P-derivation and P-multiplier. We present theorems on the structure of the factor ring R/P and the description of these mappings in some specific situations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alhmadi, F.A.A., Mamouni, A., Tamekkante, M.: A generalization of Posner’s theorem on derivations in rings. Indian J. Pure Appl. Math. 51(5), 187–194 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  2. Mamouni, A., Oukhtite, L., Zerra, M.: On derivations involving prime ideals and commutativity in rings. São Paulo J. Math. Sci. 14(2), 675–688 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  3. Mamouni, A., Oukhtite, L., Zerra, M.: Prime ideals and generalized derivations with central values on rings. Rend. Circolo Mat. Palermo Ser. (2020). https://doi.org/10.1007/s12215-020-00578-3

    Article  MATH  Google Scholar 

  4. Bell, H.E., Kappe, L.C.: Rings in which derivations satisfy certain algebraic conditions. Acta Math. Hung. 53, 339–346 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Brešar, M.: Semiderivations of prime rings. Proc. Am. Math. Soc. 108(4), 859–860 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dhara, B.: Generalized derivations acting as homomorphism or anti-homomorphism in semiprime rings. Bietr. Algebra Geom. 53(1), 203–209 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. El Mir, H., Mamouni, A., Oukhtite, L.: Commutativity with algebraic identities involving prime ideals. Commun. Korean Math. Soc. 35(3), 723–731 (2020)

    MathSciNet  MATH  Google Scholar 

  8. Rehman, N.: On generalized derivations as homomorphisms and anti-homomorphisms. Glas. Mat. 39(59), 27–30 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rehman, N., Alnoghashi, H.M.: Actions of prime ideals on generalized derivations-I, arXiv:2107.06769v1 [math.RA] 14 Jul (2021)

  10. Rehman, N., Hongan, M., Alnoghashi, H.M.: On generalized derivations involving prime ideals. Rend. Circolo Mat. Palermo Ser. (2022). https://doi.org/10.1007/s12215-021-00639-1

    Article  MATH  Google Scholar 

  11. Sandhu, G.S., Kumar, D.: Generalized derivations acting as homomorphisms or anti-homomorphisms on Lie ideals. Palest. J. Math. 7(Spl. Issue: I), 137–142 (2018)

    MathSciNet  MATH  Google Scholar 

  12. Sandhu, G.S.: Multiplicative (generalized)-derivations of prime rings that act as \(n\)-(anti)homomorphisms. Mat. Stud. 53(2), 125–133 (2020). https://doi.org/10.30970/ms.53.2.125-133

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Abdelkarim Boua and Nadeem Ur Rehman have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Patel Memorial National College, Rajpura, 140401, India

    Gurninder S. Sandhu

  2. Polydisciplinary Faculty, LSI, Sidi Mohammed Ben Abdellah University, 140401, Taza, Morocco

    Abdelkarim Boua

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Nadeem Ur Rehman

Authors
  1. Gurninder S. Sandhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdelkarim Boua
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nadeem Ur Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gurninder S. Sandhu.

Ethics declarations

Conflict of interest

We declare that there is no conflict of interest in this study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sandhu, G.S., Boua, A. & Ur Rehman, N. Some results involving P-derivations and prime ideals in rings. Ann Univ Ferrara 69, 587–604 (2023). https://doi.org/10.1007/s11565-022-00453-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11565-022-00453-2

Keywords

Mathematics Subject Classification

Search

Navigation