ON f-DERIVATIONS FROM SEMILATTICES TO LATTICES (original) (raw)
Related papers
Bulletin of the Korean Mathematical Society, 2008
In this paper, as a generalization of derivation on a lattice, the notion of f-derivation for a lattice is introduced and some related properties are investigated.
(F,G)-Derivations on a Lattice
Kragujevac journal of mathematics, 2022
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.
Generalized Symmetric Bi-Derivations of Lattices
2019
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.
Generalized Derivations of Lattices
INTERNATIONAL JOURNAL OF CONTEMPORARY …, 2010
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.
n-Derivations and (n,m)-Derivations of Lattices
Mathematics
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.
F-Fixed Points of Isotone F-Derivations on a Lattice
Discussiones Mathematicae - General Algebra and Applications, 2019
In a recent paper, Ç even andÖztürk have generalized the notion of derivation on a lattice to f-derivation, where f is a given function of that lattice into itself. Under some conditions, they have characterized the distributive and modular lattices in terms of their isotone f-derivations. In this paper, we investigate the most important properties of isotone f-derivations on a lattice, paying particular attention to the lattice (resp. ideal) structures of isotone f-derivations and the sets of their f-fixed points. As applications, we provide characterizations of distributive lattices and principal ideals of a lattice in terms of principal f-derivations.
On Symmetric Bi-Derivations of Lattice Implication Algebras
gazi university journal of science, 2017
In this paper, we introduced the notion of symmetric biderivations on lattice implication algebra and investigated some related properties. Also, we characterized the FixD(L), and KerD(L) by symmetric bi-derivations. Additionally, we proved that if D is a symmetric bi-derivation of a lattice implication algebra, every lter F is D-invariant.
A NOTE ON GENERALIZED PERMUTING f-n-DERIVATIONS IN A LATTICE
Far East Journal of Mathematical Sciences (FJMS)
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.
Symmetric Bi-T -Derivation of Lattices
2019
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
Some remarks on distributive semilattices
Commentationes Mathematicae Universitatis Carolinae
In this paper we give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we present some new ones through annihilators and relative maximal filters. We also simplify the topological representation for distributive semilattices given in [S. A. Celani, Sci. Math. Jpn. 58, No. 1, 55–65 (2003; Zbl 1041.06002)] and show that the meet-relations are closed under composition. So, we obtain that the DS-spaces with meet-relations form a category dual to the category of distributive semilattices with homomorphisms. These results complete the topological representation presented in the above-mentioned paper without the use of ordered topological spaces. Finally, following the work of G. Bezhanishvili and R. Jansana in [Order 28, No. 2, 201–220 (2011; Zbl 1243.06003)], we prove a characterization of homomorphic images of a distributive semilattice A by means of the family of closed subsets of the dual space endowed with a lo...