ON f-DERIVATIONS FROM SEMILATTICES TO LATTICES

Title & Authors
ON f-DERIVATIONS FROM SEMILATTICES TO LATTICES
Yon, Yong Ho; Kim, Kyung Ho;

Abstract
In this paper, we introduce the notion of f-derivations from a semilattice S to a lattice L, as a generalization of derivation and f-derivation 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 $\small{SD_f(S,L)}$ of all simple f-derivations on S to L for every $\small{{\wedge}}$-homomorphism $\small{f:S{\rightarrow}L}$ such that $\small{f(x_0){\vee}f(y_0)=1}$ for some $\small{x_0,y_0{\in}S}$, in particular, $\small{L{\simeq_-}=SD_f(S,L)}$ for every $\small{{\wedge}}$-homomorphism $\small{f:S{\rightarrow}L}$ such that $\small{f(x_0)=1}$ for some $\small{x_0{\in}S}$.
Keywords
semilattices;lattices;derivation;simple derivation;
Language
English
Cited by
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