Some Results on Fixed Sets and Kernel Sets of Permuting \(n\)-\((f ,g)\)-derivation of Lattices
DOI:
https://doi.org/10.26713/cma.v13i3.1870Keywords:
Lattice, Derivation, \((f,g)\)-derivation, Permuting \(n\)-\((f,g)\)-derivation, Fixed set, Kernel setAbstract
In this paper, we introduce a multivariate fixed set, a partial fixed set, a multivariate kernel set and a partial kernel set of permuting \(n\)-\((f , g)\)-derivation in lattices, and investigate some related properties. We also give some conditions under which these sets are sublattices and ideals.
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Y. Ceven and M. A. Ozturk, On f -derivations of lattices, Bulletin of the Korean Mathematical Society 45(4) (2008), 701 – 707, DOI: 10.4134/BKMS.2008.45.4.701.
Y. Çeven, Symmetric bi-derivations of lattices, Quaestiones Mathematicae 32 (2009), 241 – 245, DOI: 10.2989/QM.2009.32.2.6.799.
M. A. Chaudhry and Z. Ullah, On generalized (α,β)-derivations on lattices, Quaestiones Mathematicae 34(4) (2011), 417 – 424, DOI: 10.2989/16073606.2011.640439.
L. Ferrari, On derivations of lattices, Pure Mathematics and Applications 12 (2001), 365 – 382, URL: http://web.math.unifi.it/users/ferrari/derlat.pdf.
S. Harmaitree and U. Leerawat, On f -derivations in lattices, Far East Journal of Mathematical Sciences 51(1) (2011), 27 – 40, URL: http://www.pphmj.com/abstract/5779.html.
U. Leerawat and P. Chotchaya, On permuting n-(f , g)-derivations of lattices, International Journal of Mathematics and Computer Science 17(1) (2022), 485 – 497, URL: http://ijmcs.future-in-tech.net/17.1/R-Leerawat-Chotchaya.pdf.
R. Lidl and G. Pilz, Applied Abstract Algebra, Springer-Verlag, Inc., New York, USA (1984), DOI: 10.1007/978-1-4615-6465-2.
M. A. Öztürk, H. Yazarl and K. H. Kim, Permuting tri-derivations in lattices, Quaestiones Mathematicae 32 (2009), 415 – 425, DOI: 10.2989/QM.2009.32.3.10.911.
G. Szász, Derivations of lattices, Acta Scientiarum Mathematicarum (Szeged) 37 (1975), 149 – 154.
J. Wang, Y. Jun, X. Xin and Y. Zou, On derivations of bounded hyperlattices, Journal of Mathematical Research with Applications 36 (2016), 151 – 161, DOI: 10.3770/j.issn:2095-2651.2016.02.003.
X. L. Xin, T. Y. Liu and J. H. Lu, On derivations of lattices, Information Sciences 178(2) (2008), 307 – 316, DOI: 10.1016/j.ins.2007.08.018.
X. L. Xin, The fixed set of a derivation in lattices, Fixed Point Theory Applications (A Springer Open Journal) 218 (2012), DOI: 10.1186/16871812-2012-218.
H. Yazarli and M. A. Ozturk, Permuting tri-f -derivations in lattices, Communications of the Korean Mathematical Society 26(1) (2011), 13 – 21, DOI: 10.4134/CKMS.2011.26.1.013.
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