Some results on dependent elements in semirings
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 93-99.

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In this paper, we introduce the notion of dependent elements of derivation in MA-Semirings. We also generalize some results of dependent elements of derivation of rings for MA-Semirings.
Keywords: MA-semiring, semiprime MA-semiring, commutators, centralizer, derivation, dependent element, free action
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Sara, S.; Uzma, R. Some results on dependent elements in semirings. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 1, pp. 93-99. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_1_a5/

[1] Ali, F. and Chaudhry, M. A. Dependent elements of derivations on semiprime rings. International Journal of Mathematics and Mathematical Sciences, (2009). https://doi.org/10.1155/2009/696737

[2] Bandelt, H. J. and Petrich, M. Subdirect products of rings and distributive lattices. Proceedings of the Edinburgh Mathematical Society, 25(2): 155-171 (1982). https://doi.org/10.1017/s0013091500016643

[3] Chaudhry, M. A. and Samman, M. S. Free actions on semiprime rings. Mathematica Bohemica, 133(2): 197-208 (2008). https://doi.org/10.21136/mb.2008.134055

[4] Golan, J. The Theory of Semirings with Application in Math. and Theoretical Computer Science, (Vol. 54), Monographs and Surveys in Pure and Applied Mathematics. (1992).

[5] Javed, M. A. and Aslam, M. Some commutativity conditions in prime MA-semirings. ARS COMBINATORIA, 114: 373-384 (2014).

[6] Javed, M. A., Aslam, M. and Hussain, M. On condition (A2) of Bandlet and Petrich for inverse semirings. In Int. Math. Forum, 7(59): 2903-2914 (2012).

[7] Kallman, R. R. A generalization of free action. Duke Mathematical Journal, 36(4): 781-789 (1969). http://gdmltest.u-ga.fr/item/1077378641/

[8] Karvellas, P. H. Inversive semirings. Journal of the Australian Mathematical Society, 18(3): 277-288 (1974). https://doi.org/10.1215/s0012-7094-69-03693-x

[9] Murray, F. J. and von Neumann, J. On rings of operators. II. Transactions of the American Mathematical Society, 41(2): 208-248 (1937).

[10] Murugesan, R., Sindhu, K. K. and Namasivayam, P. Free Actions of Semi derivations on Semiprime Semirings. International Journal of Science and Engineering Invention, 2(04): (2016).

[11] Sara, S., Aslam, M. and Javed, M. A. On dependent elements and free actions in inverse semirings. In Int. Math. Forum, 12: 557-564 (2016). https://doi.org/10.12988/imf.2016.6441

[12] Sara, S., Aslam, M. and Javed, M. On centralizer of semiprime inverse semiring. Discussiones Mathematicae-General Algebra and Applications, 36(1): 71-84 (2016). https://doi.org/10.7151/dmgaa.1252

[13] S. Sara and M. Aslam, On Posners Second theorem in additively inverse semiring, Hacettepe Journal of Mathematics and Statistics, 48(4) (2019), 996-1000. https://doi.org/10.15672/hjms.2018.576

[14] S. Sara and M. Aslam, On Lie ideals of Inverse Semirings, Italian Journal of Pure and Applied Mathematics, 44 (2020), 22-29. https://doi.org/10.1142/s1793557121501813

[15] Thaheem, A. On dependent elements in semiprime rings. Mathematica Japonicae, 47(1): 29-31 (1998).

[16] Vukman, J. and Kosi-Ulbl, I. On dependent elements in rings. International Journal of Mathematics and Mathematical Sciences, 54: 2895-2906 (2004). https://doi.org/10.1155/s0161171204311221