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Left Jordan derivations on certain semirings

Year 2021, Volume: 50 Issue: 3, 624 - 633, 07.06.2021
https://doi.org/10.15672/hujms.491343

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 $S$.

References

  • [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.
Year 2021, Volume: 50 Issue: 3, 624 - 633, 07.06.2021
https://doi.org/10.15672/hujms.491343

Abstract

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Yaqoub Ahmed 0000-0001-9033-0916

Wieslaw Dudek This is me 0000-0001-8919-7249

Publication Date June 7, 2021
Published in Issue Year 2021 Volume: 50 Issue: 3

Cite

APA Ahmed, Y., & Dudek, W. (2021). Left Jordan derivations on certain semirings. Hacettepe Journal of Mathematics and Statistics, 50(3), 624-633. https://doi.org/10.15672/hujms.491343
AMA Ahmed Y, Dudek W. Left Jordan derivations on certain semirings. Hacettepe Journal of Mathematics and Statistics. June 2021;50(3):624-633. doi:10.15672/hujms.491343
Chicago Ahmed, Yaqoub, and Wieslaw Dudek. “Left Jordan Derivations on Certain Semirings”. Hacettepe Journal of Mathematics and Statistics 50, no. 3 (June 2021): 624-33. https://doi.org/10.15672/hujms.491343.
EndNote Ahmed Y, Dudek W (June 1, 2021) Left Jordan derivations on certain semirings. Hacettepe Journal of Mathematics and Statistics 50 3 624–633.
IEEE Y. Ahmed and W. Dudek, “Left Jordan derivations on certain semirings”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 624–633, 2021, doi: 10.15672/hujms.491343.
ISNAD Ahmed, Yaqoub - Dudek, Wieslaw. “Left Jordan Derivations on Certain Semirings”. Hacettepe Journal of Mathematics and Statistics 50/3 (June 2021), 624-633. https://doi.org/10.15672/hujms.491343.
JAMA Ahmed Y, Dudek W. Left Jordan derivations on certain semirings. Hacettepe Journal of Mathematics and Statistics. 2021;50:624–633.
MLA Ahmed, Yaqoub and Wieslaw Dudek. “Left Jordan Derivations on Certain Semirings”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, 2021, pp. 624-33, doi:10.15672/hujms.491343.
Vancouver Ahmed Y, Dudek W. Left Jordan derivations on certain semirings. Hacettepe Journal of Mathematics and Statistics. 2021;50(3):624-33.