Semilattices of bisimple inverse semigroups.
Semilattices of finite arithmetical algebras
Semilattices of groups with distributive congruence lattice.
Semilattices of width 3 whose decomposable elements form a chain.
Semilattices which must contain a copy of 2 N.
Semilattices with sectional mappings
We consider join-semilattices with 1 where for every element p a mapping on the interval [p,1] is defined; these mappings are called sectional mappings and such structures are called semilattices with sectional mappings. We assign to every semilattice with sectional mappings a binary operation which enables us to classify the cases where the sectional mappings are involutions and / or antitone mappings. The paper generalizes results of [3] and [4], and there are also some connections to [1].
Semimatroids and their Tutte polynomials.
Semi-valuation et métrique associée
Some remarks on certain classes of semilattices.
Some remarks on distributive semilattices
In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....
Strong elements in lattices
Subdirectly irreducible decomposition of some algebras having the semilattice structure
Subdirectly irreducible sectionally pseudocomplemented semilattices
Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented...
Subdirectly irreducible semilattices with an automorphism.
Subdirectly Irreducibles in some Varieties of Algebras having the Semilattice Structure
Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues
For a Tikhonov space X we denote by Pc(X) the semilattice of all continuous pseudometrics on X. It is proved that compact Hausdorff spaces X and Y are homeomorphic if and only if there is a positive-homogeneous (or an additive) semi-lattice isomorphism T:Pc(X) → Pc(Y). A topology on Pc(X) is called admissible if it is intermediate between the compact-open and pointwise topologies on Pc(X). Another result states that Tikhonov spaces X and Y are homeomorphic if and only if there exists a positive-homogeneous...
Tail and free poset algebras.
We characterize free poset algebras F(P) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F(P) is established. Moreover, a characterization of upper semi-lattice algebras that are isomorphic to free poset algebras is given in terms of a selected set of generators of B(T).
The algebra of mode homomorphisms
Modes are idempotent and entropic algebras. While the mode structure of sets of submodes has received considerable attention in the past, this paper is devoted to the study of mode structure on sets of mode homomorphisms. Connections between the two constructions are established. A detailed analysis is given for the algebra of homomorphisms from submodes of one mode to submodes of another. In particular, it is shown that such algebras can be decomposed as Płonka sums of more elementary homomorphism...
The graphs of join-semilattices and the shape of congruence lattices of particle lattices
We attach to each -semilattice a graph whose vertices are join-irreducible elements of and whose edges correspond to the reflexive dependency relation. We study properties of the graph both when is a join-semilattice and when it is a lattice. We call a -semilattice particle provided that the set of its join-irreducible elements satisfies DCC and join-generates . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...
The ideal structure of simple ternary algebras