References
- L. Ali, M. Aslam, G. Farid and S.A. Khalek, On differential identities of Jordan ideals of semirings, Aims Math. 6 (2020), 6833-6844. DOI:10.3934/math.2021400
- L. Ali, Y.A. Khan, A.A. Mousa, S.A. Khalek and G. Farid, Some differential identities of MA-semirings with involution, Aims Math. 6 (2020), 2304-2314. DOI:10.3934/math.2021139
- L. Ali , M. Aslam and Y.A. Khan, Some results on commutativity of MA-semirings, Indian J. Sci. Technol. 13 (2020), 3198-3203. https://doi.org/10.17485/IJST/v13i31.1022
- L. Ali, M. Aslam and Y.A. Khan, Commutativity of semirings with involution, Asian-Eur. J. Math. (2019), 8 pages. DOI:10.1142/S1793557120501533
- S. Ali, A.N.A. Koam and M.A. Ansari, On *-differential identities in prime rings with involution, Hacet. J. Math. Stat. 49 (2020), 708-715. DOI:10.15672/hujms.588726
- A.I. Barvinok, Combinatorial Optimization and Computations in the Ring of Polynomials, DIMACS Technical Report, 1993, 93-103.
- S. Bistarelli, Semirings for Soft Constraint Solving and Programming, Springer-Verlag, Berlin, 2004.
- M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93. https://doi.org/10.1017/S0017089500008077
- N.A. Dar and S. Ali, On *-commuting mappings and derivations in rings with involution, Turk. J. Math. 40 (2016), 884-894. https://doi.org/10.3906/mat-1508-61
- M. Droste, W. Kuich and H. Vogler, Handbook of Weighted Automata, EATCS Monographs in Theoretical Computer Science, Springer, Berlin, 2009.
- S. Eilenberg, Automata, Languages, and Machines, Academic Press, New York, vol. A, 1974.
- Z. Esik, W. Kuich, Modern Automata Theory, Institut fur Diskrete Mathematik und Geometrie, 2012. doi.org/10.34726/2481
- K. Glazek, A guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences with complete bibliography, Kluwer Academic Publishers, Dordrecht, 2002.
- J.S. Golan, Semirings and their Applications, Kluwer Acad. Pub., Dodrecht, 1999.
- U. Hebisch, H.J. Weinert, Semirings: Algebraic theory and applications in computer science, World Scientific 1998.
- I.N. Herstein, A note on derivation II, Canad. Math. Bull. 22 (1979), 509-511. https://doi.org/10.4153/CMB-1979-066-2
- J.M. Howie, Automata and Languages, Clarendon Press, Oxford, 1991.
- M.A. Javed, M. Aslam and M. Hussain, On condition (A2) of Bandlet and Petrich for inverse semiqrings, Int. Math. Forum 07 (2012), 2903-2914.
- B.E. Johnson, Continuity of derivations on commutative Banach algebras, AM. J. MATH. 91 (1969), 1-10. https://doi.org/10.2307/2373262
- D.A. Jordan, On the ideals of a Lie algebra of derivations, J. Lond. Math. Soc. 02 (1986), 33-39. https://doi.org/10.1112/jlms/s2-33.1.33
- Y.A. Khan, M. Aslam and L. Ali, Commutativity of additive inverse semirings through f(xy) = [x,f(y)], Thai J. Math. (2018), 288-300.
- V.N. Kolokoltsov, V.P. Maslov, Idempotent analysis and its applications, Kluwer Acad. Publ. Dordrecht, 1997, 243-302.
- C. Lanski, Commutation with skew elements in rings with involution, Pac. J. Math. 83 (1979), 393-399. https://doi.org/10.2140/pjm.1979.83.393
- T.K Lee, On derivations of prime rings with involution, Chin. J. Math. 20 (1992), 191-203.
- V.P. Maslov, S.N. Samborskii, Idempotent analysis, Adv. in Sov. Math. 13 (1992), AMS, RI.
- E.C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 08 (1957), 1093-1100. https://doi.org/10.1090/S0002-9939-1957-0095863-0
- C.E. Rickart, Banach algebras with an adjoint operation, Ann. Math. 47 (1946), 528-550. https://doi.org/10.2307/1969091
- I.E. Segal, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. 53 (1947), 73-88. https://doi.org/10.1090/S0002-9904-1947-08742-5
- S. Shafiq, M. Aslam and M.A. Javed, On centralizer of semiprime inverse semiring, Discuss. Math. Gen. Algebra Appl. 36 (2016), 71-84. https://doi.org/10.7151/dmgaa.1252
- S. Shafiq and M. Aslam, A study of MA-semirings, PhD Thesis, GC University Lahore, Pakistan, 2019.