On additive maps of MA-semirings with involution





MA-semirings, *-semirings, *-derivations, Jordan *- derivations


We extend the concept of *-derivations of rings to a certain class of semirings called MA-semirings and establish some results on commutativity forced by the *-derivations satisfying different criteria. We specially focus on the results on certain conditions under which additive mappings become Jordan *-derivations.

Author Biographies

Liaqat Ali, Government College University.

Dept. of Mathematics.

Muhammad Aslam, Government College University.

Dept. of Mathematics.

Yaqoub Ahmed Khan, Government College University.

Dept. of Mathematics.


L. Ali, M. Aslam, and Y. A. Khan, “Commutativity of semirings with involution”, Asian-European journal of mathematics, Art ID. 2050153, 2019, doi: 10.1142/S1793557120501533

L. Ali, M. Aslam, and Y. A. Khan, “On Jordan ideals of inverse semirings with involution”, Indian journal of science and technology, vol. 13, no, 4, pp. 430-438, 2020- [On line]. Available: https://bit.ly/2ZrljRb

L. Ali, M. Aslam, and Y. A. Khan, “Some commutativity conditions on *-prime semirings”, JP journal of algebra, number theory and applications, vol. 46, no. 2, pp. 109-121, May 2020, doi: 10.17654/NT046020109

L. Ali, M. Aslam, and Y. A. Khan, “On generalized derivations of semirings with involution”, Journal of mechanics continua and mathematical sciences, vol. 15, no. 4, Apr. 2020, doi: 10.26782/jmcms.2020.04.00011

K. I. Beidar and W. S. Martindale, “On functional identities in prime rings with involution”, Journal of algebra, vol. 203, no. 2, pp. 491-532, May 1998, doi: 10.1006/jabr.1997.7285

M. Brešar and J. Vukman, “On some additive mappings in rings with involution”, Aequationes mathematics, vol. 38, no. 2-3, pp. 178-185, Jun. 1989, doi: 10.1007/BF01840003

I. N. Herstein, Rings with involution, Chicago, IL: University of Chicago, 1976.

M. A. Javed, M. Aslam, and M. Hussain, “On condition (A2) of Bandlet and Petrich for inverse semirings”, International mathematical forum, vol. 7, no. 59, pp. 2903-2914, 2012. [On line]. Available: https://bit.ly/3fqASOw

Y. A. Khan, M. Aslam, and L. Ali, “Commutativity of additive inverse semirings through f(xy) = [x,f(y)]”, Thai journal of mathematics, special issue, pp. 288-300, 2018. [On line]. Available: https://bit.ly/38RgRhz

K. H. Kim and Y. H. Lee, “A note on *-derivation of *-prime rings”, International mathematical forum, vol. 12, no. 8, pp. 391-398, 2017, doi: 10.12988/imf.2017.7114

C. Lanski, “Commutation with skew elements in rings with involution”, Pacific journal of mathematics, vol. 83, no. 2, pp. 393-399, Aug. 1979, doi: 10.2140/pjm.1979.83.393

T. K. Lee and P. Y. Shen, “On derivations of prime rings with involution”, Chinese journal of mathematics, vol. 20, no. 2, pp. 191-203, Jun. 1992. [On line]. Available: https://bit.ly/2ZnI4oP

L. Oukhtite and S. Salhi, “On derivations in ?-prime rings”, International journal of algebra, vol. 1, no. 5, pp. 241-246, 2007, doi: 10.12988/ija.2007.07025

T. W. Palmer, Banach algebras and the general theory of *-algebras, vol. 2. Cambridge: Cambridge University Press, 2001, doi: 10.1017/CBO9780511574757

S. Sara, M. Aslam, and M. A Javed, “On centralizer of semiprime inverse semiring”, Discussiones mathematicae - General algebra and applications, vol. 36, no.1, pp. 71-84, 2016, doi: 10.7151/dmgaa.1252

I. E. Segal, “Irreducible representations of operator algebras”, Bulletin American Mathematics and Society, vol. 53, pp. 73-88, Feb. 1947, doi: 10.1090/S0002-9904-1947-08742-5



How to Cite

L. Ali, M. Aslam, and Y. A. Khan, “On additive maps of MA-semirings with involution”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 1097-1112, Jul. 2020.