SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

Left Jordan derivations on certain semirings

Yaqoub AHMED
Wieslaw A. DUDEK
Pages
624–633
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is a left derivation on this semiring and prove when a left Jordan derivation on $S$ implies the commutativity of $S$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is a left derivation on this semiring and prove when a left Jordan derivation on $S$ implies the commutativity of $S$.
📊
Key Findings & Data:We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is a left derivation on this semiring and prove when a left Jordan derivation on $S$ implies the commutativity of $S$.
💡
Conclusion & Impact:We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is a left derivation on this semiring and prove when a left Jordan derivation on $S$ implies the commutativity of $S$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Left derivation · Jordan derivation · inverse semiring

Abstract

We determine conditions under which a left Jordan derivation defined on an $MA$-semiring $S$ is a left derivation on this semiring and prove when a left Jordan derivation on $S$ implies the commutativity of $S$.

🔖

Cite This Article

AHMED, Y., DUDEK, W. A. (2022). Left Jordan derivations on certain semirings. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 624–633. https://ajindex.com/articles/529438

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Y. Ahmed and W.A. Dudek, Stronger Lie derivations on $MA$-semirings, Afrika Mat. 31 (5-6), 891-901, 2020
  2. S. Ali, M. Ashraf, M.S. Khan and J. Vukman, Commutativity of rings involving additive mappings, Quaest. Math. 37 (2), 215-229, 2014
  3. M. Ashraf and N.U. Rehmann, On Lie ideals and Jordan left derivations of prime rings, Arch. Math. (Brno) 36, 201-206, 2000
  4. M. Ashraf and N.U. Rehmann, On commutativity of rings with derivations, Results Math. 42, 3-8, 2002
  5. R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc. 90, 9-14, 1984
  6. H.E. Bell and J. Lucier, On additive maps and commutativity in rings, Results Math. 36, 1-8, 1999
  7. M. Brešar and J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc., 110, 7-16, 1990
  8. W.A. Dudek, M. Shabir and R. Anjum, Characterizations of hemirings by their hideals, Comput. Math. Appl. 59 (9), 3167-3179, 2010
  9. K. Glazek, A Guide to Literature on Semirings and their Applications in Mathematics and Information Sciences with Complete Bibliography, Kluwer Acad. Publ., Dodrecht, 2002
  10. J.S. Golan, Semirings and their Applications, Kluwer Acad. Publ. 1999
  11. M.A. Javed, M. Aslam and M. Hussain, On condition $(A_{2})$ of Bandelt and Petrich for inverse semirings, Int. Math. Forum 7, 2903-2914, 2012
  12. P.H. Karvellas, Inversive semirings, J. Austral. Math. Soc. 18, 277-288, 1974
  13. M. Nadeem, M. Aslam, On the generalization of Brešar theorems, Quasigroups and Related Systems 24, 123-128, 2016
  14. E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8, 1093-1100, 1957
  15. S. Shafiq and M. Aslam, Centralizers on semiprime MA-semirings, Quasigroups and Related Systems 24, 269-276, 2016
  16. S. Shafiq and M. Aslam, On Jordan mappings of inverse semirings, Open Math. 17, 1123-1131, 2017
  17. J. Vukman, On left Jordan derivations of rings and Banach algebras, Aequationes Math. 75, 260-266 2008
  18. J. Zhan and W.A. Dudek, Fuzzy h-ideals of hemirings, Inform. Sci. 177 (3), 876-886, 2007.