Some results on Lattice involving generalized permuting tri-derivations
Abstract
In this paper we introduce the notion of generalized permuting tri-derivations, g-derivations, and g-tri-derivations on lattices, and we study and generalize some properties discussed in [14] and [29]. We also give some properties characterizing the g-derivations, the g-tri-derivations, and the generalized permuting tri-derivations and their trace.
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References
G. Birkhoff, Lattice Theory, Amer. Math. Soc., New York, 1940.
E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
C. Degang, Z. Wenxiu, D. Yeung, E. C. C. Tsang, Rough approximations on a complete distributive lattice with applications to generalized rough sets, Inform. Sci., 176 (2006), 1829-1848.
F. Karacal, On the direct decomposability of strong negations and S-implication operators on product lattices, Inform. Sci., 176 (2006), 3011-3025.
B. Havala, Generalized derivations in rings, Comm. Algebra., 26 (4) (1998), 1147-1166.
H. E. Bell, L.C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar., 53 (3.4) (1989), 339-346.
G. F. Birkenmeier, M. Ghirati, and A. Taherifar. (2015). When is a sum of annihilator ideals an annihilator ideal?. Commun. Algebra. 43: 2690–2702.
K. Kaya, Prime rings with - derivations, Bull. Nat. Sci. Eng., 16, (1988) 63-71.
M. A. Oztürk, Permuting Tri-derivations in Prime and Semi-prime Rings, East Asian Math. J., 15 (1999), 177–190.
M. Bresar, On the distance of the composition of the two derivations to the generalized derivations, Glasg. Math. J., 33 (1991), 89-93.
R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, United States, 1974.
R. S. Sandhu, Role hierarchies and constraints for lattice-based access controls, Proceedings of the 4th European Symposium on Research in Computer Security, Rome, Italy, (1996), 6-79
A. Honda, and M. Grabisch, Entropy of capacities on lattices and set systems, Inform. Sci., 176 (2006), 3472-3489.
Y. çeven, On characterizations of Lattices using the generalized symmetric bi-derivations, Bull. Int. Math. Virtual Inst, 9 (2019), 95-102.
A. J. Bell, The co-information lattice, in: 4th International Symposium on Independent Component Analysis and Blind Signal Separation ICA, 2003 (2003), 921-926.
C. Carpineto, G. Romano, Information retrieval through hybrid navigation of lattice representations, Int. J. Hum Computst, 45 (1996), 553-578.
T. Dube and A. Taherifar, On the lattice of annihilator ideals and its applications, Communications in Algebra, 49(6), 2021, 2444–2456.
G. Durfee, Cryptanalysis of RSA using algebraic and lattice methods, Ph. D. Dissertation, Department of computer science, Stanford University, 2002.
G. Szász, Derivations of lattices, Acta Sci. Math., 37 (1975), 149–154.
X. L. Xin, T. Y. Li and J. H. Lu, On derivations of lattices, Inform. Sci., 178 (2008), 307–316.
L. Ferrari, On derivations of lattices, Pure Math. Appl., 12 (2001), 365–382.
Y. S. Jung, and K. H. Park,On prime and semiprime rings with permuting 3-derivations, Bull. Korean Math. Soc., 44 (2007), 789–794.
K. H. Park, On prime and semiprime rings with symmetric n-derivations, J. Chungcheong Math. Soc., 22 (2009), 451–458.
J. Vukman, Symmetric bi-derivations on prime and semi-prime rings, Aequ. Math. 38 (1989), 245–254.
N. Argaç, and E. Albas, Generalized derivations of prime rings, Algebra Coll., 11 (2004), 399-410.
M. A. Oztürk, and M. Sapancy, On generalized symmetric bi-derivations in prime rings, East Asian Math. J., 15(2) (1999), 165-176.
N. O. Alshehri. Generalized derivation of lattices, Int. J. Contemp. Math. Sci., 5 (13) (2010), 629–640.
Y. Çeven. Symmetric bi-derivations of lattices, Quaest. Math., 32 (2009), 241-245.
M. A. Oztürk, H. Yazarl and K. H. Kim. Permuting tri-derivations in lattices, Quaest. Math., 32(3) (2009), 415-425.
Y. Çeven, n-Derivations and (n,m)-Derivations of Lattices, Mathematics, 6 12 (2018), 307.
Y. B. Jun and X. L. Xin, On derivations of BCI-algebras, Inform. Sci., 159 (2004), 167–176.
C. Jana, T. Senapati, and M. Pal, Derivation, f-derivation and generalized derivation of KUS-algebras, Cogent Mathematics, 2 (2015), 1-12.
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