Skip to main content
Log in

Nonexistence of nonzero derivations on some classes of zero-symmetric 3-prime near-rings

  • Published:
Ukrainian Mathematical Journal Aims and scope

We give some classes of zero-symmetric 3-prime near-rings such that every member of these classes has no nonzero derivation. Moreover, we extend the concept of “3-prime” to subsets of near-rings and use it to generalize Theorem 1.1 due to Fong, Ke, and Wang concerning the transformation near-rings M o (G) by using a different technique and a simpler proof.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. H. E. Bell and N. Argac, “Derivations, products of derivations, and commutativity in near-rings,” Algebra Colloq., 8, 399–407 (2001).

    MATH  MathSciNet  Google Scholar 

  2. H. E. Bell and G. Mason, “On derivations in near-rings,” Proc. Near-rings and Near-fields, G. Betsch, et al. (eds.), North-Holland Math. Stud. (1987), pp. 31–35.

  3. Y. Fong, W.-F. Ke, and C.-S. Wang, “Nonexistence of derivations on transformation near-rings,” Comm. Algebra, 28, 1423–1428 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  4. T. W. Hungerford, Algebra, Holt, Rinehart, and Winston, Inc., New York (1974).

    Google Scholar 

  5. A. M. Kamal Ahmed and H. Al-Shaalan Khalid, “Existence of derivations on near-rings,” Math. Slovaca, 63, No. 3, 431–448 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  6. J. D. P. Meldrum, Near-Rings and Their Links with Groups, Pitman, Boston, MA (1985).

    Google Scholar 

  7. G. Pilz, Near-Rings, North-Holland, Amsterdam (1983).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 3, pp. 420–424, March, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamal, A.A.M., Al-Shaalan, K.H. Nonexistence of nonzero derivations on some classes of zero-symmetric 3-prime near-rings. Ukr Math J 66, 473–478 (2014). https://doi.org/10.1007/s11253-014-0945-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-014-0945-4

Keywords

Navigation