Distributive Lattices with a given Skeleton
نویسندگان
چکیده
We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.
منابع مشابه
Products of Skeletons of Finite Distributive Lattices
We prove that the skeleton of a product of finitely many finite distributive lattices is isomorphic to the product of skeletons of its factors. Thus, it is possible to construct finite distributive lattices with a given directly reducible skeleton by reducing the problem to the skeleton factors. Although not all possible lattices can be obtained this way, we show that it works for the smallest ...
متن کاملFUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES
The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...
متن کاملDistributive lattices with strong endomorphism kernel property as direct sums
Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (which are introduced after Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of ...
متن کاملA categorical equivalence for distributive Stonean residuated lattices
Stonean residuated lattices are closely related to Stone algebras since the bounded lattice reduct of a distributive Stonean residuated lattice is a Stone algebra. In the present work we follow the ideas presented by Chen and Grätzer and try to apply them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its a...
متن کاملDistributive Lattices of λ-simple Semirings
In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transit...
متن کامل