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 $S$.
[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.
[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.
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.