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http://dx.doi.org/10.11568/kjm.2019.27.2.425

A NOTE ON MULTIPLIERS IN ALMOST DISTRIBUTIVE LATTICES  

Kim, Kyung Ho (Department of Mathematics Korea National University of Transportation)
Publication Information
Korean Journal of Mathematics / v.27, no.2, 2019 , pp. 425-435 More about this Journal
Abstract
The notion of multiplier for an almost distributive lattice is introduced, and some related properties are investigated. Moreover, we introduce a congruence relation ${\phi}_{\alpha}$ induced by ${\alpha}{\in}L$ on an almost distributive lattice and derive some useful properties of ${\phi}_{\alpha}$.
Keywords
Almost distributive lattice; multiplier; isotone; idempotent; $Fix_f(L)$;
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1 H. E. Bell, L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar 53 (3-4) (1989), 339-346.   DOI
2 G. Birkhoof, Lattice Theory, American Mathematical Society, New York, 1940.
3 M. Bresar, On the distance of the composition of the derivations to the generalized derivations, Glasgow Math. J. 33 (1) (1991), 89-93.   DOI
4 A. Honda and M. Grabisch, Entropy of capacities on lattices and set systems, Information Science 176 (2006), 3472-3489.   DOI
5 F. Karacal, On the direct decomposability of strong negations and simplication operations on product lattices, Information Science 176 (2006), 3011-3025.   DOI
6 K. Kaya, Prime rings with a derivations, Bull. Master. Sci.Eng 16 (1987), 63-71.
7 L. Larsen, An Introduction to the Theory of Multipliers, Springer-Verlag, 1971.
8 E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc 8 (1957), 1093-1100.   DOI
9 U. M. Swamy and G. C. Rao, Almost Distributive lattices, J. Aust. Math. Soc.(Series A) 31 (1981), 77-91.   DOI
10 X. L. Xin, T. Y. Li and J. H. Lu, On the derivations of lattices, Information Sci., 178 (2) (2008), 307-316.   DOI