Some generalizations of derivations in posets
*Ahmed AbdelwanisCorresponding authorayunis@sci.cu.edu.egDepartment of MathematicsFaculty of ScienceCairo UniversityGiza, 12613, Egypt0000-0001-5236-5966View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 May 2024
- Published Online:
- 06 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2186
- Pages:
- 1135–1149
Abstract
Keywords
Subject Classifications
References
[1] J. Bergen, “Derivations in prime rings,” Canad. Math. Bull., vol. 26, no. 3, pp. 267–270 (1983).
[2] H. E. Bell and L. C. Kappe, “Rings in which derivations satisfy certain algebraic conditions,” Acta Math. Hungar., vol. 53, pp. 339–346 (1989).
[3] M. Brešar and J. Vukman, “Jordan derivations on prime rings,” Bull. Austral. Math. Soc., vol. 37, pp. 321–322 (1988).
[4] C.-L. Chuang, “On compositions of derivations of prime rings,” Proc. Amer. Math. Soc., vol. 108, no. 3, pp. 647–652 (1990).
[5] B. Felzenszwalb, “Derivations in prime rings,” Proc. Amer. Math. Soc., vol. 84, no. 1, pp. 16–20 (1982).
[6] S. Huang and B. Davvaz, “Generalized derivations of rings and Banach algebras,” Commun. Algebra, vol. 41, no. 3, pp. 1188–1194 (2013).
[7] Y. B. Jun and X. L. Xin, “On derivations of BCI-algebras,” Inform. Sci., vol. 159, pp. 167–176 (2004).
[8] G. F. Leger, “Generalized derivations of Lie algebras,” J. Algebra, vol. 228, pp. 165–203 (2000).
[9] X.-K. Wang, “Derivations in prime near-rings,” Proc. Amer. Math. Soc., vol. 121, no. 2, pp. 361–366 (1994).
[10] I. N. Herstein, “Jordan derivations of prime rings,” Proc. Amer. Math. Soc., vol. 8, pp. 1104–1110 (1957).
[11] E. Posner, “Derivations in prime rings,” Proc. Amer. Math. Soc., vol. 8, pp. 1093–1100 (1957).
[12] M. Asci and S. Ceran, “Generalized (f,g)-derivations of lattices,” Math. Sci. Appl. E-Notes, vol. 1, pp. 56–62 (2013).
[13] A. Amroune, L. Zedam, and M. Yettou, “(F,G)-Derivations on a lattice,” Kragujevac J. Math., vol. 46, no. 5, pp. 773–787 (2022).
[14] Y. Ceven and M. A. Öztürk, “On f-derivations of lattices,” Bull. Korean Math. Soc., vol. 45, pp. 701–707 (2008).
[15] M. A. Chaudhry and Z. Ullah, “On generalized (β,γ)-derivations on lattices,” Quaest. Math., vol. 34, pp. 417–424 (2011).
[16] L. Ferrari, “On derivations of lattices,” Pure Math. Appl., vol. 12, pp. 365–382 (2001).
[17] P. He, X. L. Xin, and J. Zhan, “On derivations and their fixed point sets in residuated lattices,” Fuzzy Sets Syst., vol. 303, pp. 97–113 (2016).
[18] G. Szász, “Derivations of lattices,” Acta Sci. Math. (Szeged), vol. 37, pp. 149–154 (1975).
[19] X. L. Xin, T. Y. Li, and J. H. Lu, “On derivations of lattices,” Inform. Sci., vol. 178, pp. 307–316 (2008).
[20] X. L. Xin, “The fixed set of a derivation in lattices,” Fixed Point Theory Appl., vol. 1, pp. 1–12 (2012).
[21] H. Zhang and Q. Li, “On derivations of partially ordered sets,” Math. Slovaca, vol. 67, no. 1, pp. 17–22 (2017).
[22] A. Y. Abdelwanis and S. Ali, “Skew derivations on partially ordered sets,” Indian J. Pure Appl. Math., vol. 52, pp. 1256–1262 (2021).
[23] A. Y. Abdelwanis and A. Boua, “On generalized derivations of partially ordered sets,” Commun. Math., vol. 27, pp. 69–78 (2019).
[24] T. Albu and M. L. Teply, “Generalized deviation of posets and modular lattices,” Discrete Math., vol. 214, pp. 1–19 (2000).
[25] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott, Continuous Lattices and Domains, Cambridge: Cambridge Univ. Press (2003).
[26] J. Larmerová and J. Rachůnek, “Translations of distributive and modular ordered sets,” Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., vol. 27, pp. 13–23 (1988).
