If G is a semisimple Lie group of real rank at least two and Γ is an irreducible lattice in G, then every homomorphism from Γ to the outer automorphism group of a finitely generated free group has finite image.

We say that a 〈∨, 0〉-semilattice S is conditionally co-Brouwerian, if (1) for all nonempty subsets X and Y of S such that X ≤ Y (i.e., x ≤ y for all 〈x, y〉 ∈ X × Y ), there exists z ∈ S such that X ≤ z ≤ Y , and (2) for every subset Z of S and all a, b ∈ S, if a ≤ b ∨ z for all z ∈ Z, then there exists c ∈ S such that a ≤ b ∨ c and c ≤ Z. By restricting this definition to subsets X , Y , and Z ...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

This article presets a review of the achievements rapidly developing field of cryptography - public-key cryptography based on the lattice theory. Paper contains the necessary basic concepts and the major problems of the lattice theory, as well as together with the description on the benefits of this cryptography class - the properties of the reliability to quantum computers and full homomorphis...

A graph homomorphism from a graph G to a graph H is a mapping h : V (G)→ V (H) such that h(u) ∼ h(v) if u ∼ v. Graph homomorphisms are well studied objects and, for suitable choices of eitherG orH, many classical graph properties can be formulated in terms of homomorphisms. For example the question of wether there exists a homomorphism from G to H = Kq is the same as asking wether G is q-colour...

The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruence...

In this paper, we investigate how it is possible to define a new class of lattice gauge models based on dualization procedure previous generalization the Kitaev Quantum Double Models. case that will be used as basis, was defined by adding qudits (which were denoted matter fields in reference some works) vertices with intention of, for instance, interpreting its Models coupled Potts ones. Now, r...

Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper is an attempt to initiate a relatively systematic study of locally solid topological lattice-ordered groups. We give both Roberts-Namioka-type characterization and Fremlin-type characterization of locally solid topolo...

Motivated by the Lipschitz-lifting property of Banach spaces introduced Godefroy and Kalton, we consider lattice-lifting property, which is an analogous notion within category lattices lattice homomorphisms. Namely, a X satisfies if every homomorphism to having bounded linear right-inverse must have right-inverse. In terms free lattices, this can be rephrased into following question: embed they...