F-Fixed Points of Isotone F-Derivations on a Lattice (original) (raw)
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In this article, the notion of a new kind of derivation is introduced for a lattice L called symmetric bi-(T, F )-derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi(T, F )-derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-(T, F )-derivation.
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The notion of generalized derivation for a lattice is introduced, and some related properties are investigated. Using the idea of isotone generalized derivation, we give characterizations of a modular lattices and distributive lattices.
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In the present paper, we introduce the notion of (F, G)-derivation on a lattice as a generalization of the notion of (∧, ∨)-derivation. This newly notion is based on two arbitrary binary operations F and G instead of the meet (∧) and the join (∨) operations. Also, we investigate properties of (F, G)-derivation on a lattice in details. Furthermore, we define and study the notion of principal (F, G)derivations as a particular class of (F, G)-derivations. As applications, we provide two representations of a given lattice in terms of its principal (F, G)-derivations.
Symmetric Bi-T -Derivation of Lattices
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In this paper, the notion of a new kind of derivation is introduced for a lattice (L,∨,∧), called symmetric bi-T -derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi-T -derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-T -derivation on L. Keyword: Lattice, Derivation of lattice, Symmetric bi-T -derivation of lattice, Modular lattice and Distributive lattice. AMS Subject Classification: 03G16, 06C05, 17A36
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In this paper, we introduce the notion of generalized permuting f-n-derivation on lattices and investigate some related properties. We characterize the distributive and modular lattices by generalized permuting f-n-derivations.
ON f-DERIVATIONS FROM SEMILATTICES TO LATTICES
Communications of the Korean Mathematical Society, 2014
In this paper, we introduce the notion of f-derivations from a semilattice S to a lattice L, as a generalization of derivation and fderivation of lattices. Also, we define the simple f-derivation from S to L, and research the properties of them and the conditions for a lattice L to be distributive. Finally, we prove that a distributive lattice L is isomorphic to the class SD f (S, L) of all simple f-derivations on S to L for every ∧-homomorphism f : S → L such that f (x 0) ∨ f (y 0) = 1 for some x 0 , y 0 ∈ S, in particular, L ∼ = SD f (S, L) for every ∧-homomorphism f : S → L such that f (x 0) = 1 for some x 0 ∈ S.
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In this paper, firstly, as a generalization of derivations on a lattice, the notion of n-derivation is introduced and some fundamental properties are investigated. Secondly, the concept of (n,m)-derivation-homomorphism on lattices is described and important and characteristic properties are given.